Download or read book Randomness and Recurrence in Dynamical Systems A Real Analysis Approach written by Rodney Nillsen and published by American Mathematical Soc.. This book was released on 2010-12-31 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Randomness and Recurrence in Dynamical Systems aims to bridge a gap between undergraduate teaching and the research level in mathematical analysis. It makes ideas on averaging, randomness, and recurrence, which traditionally require measure theory, accessible at the undergraduate and lower graduate level. The author develops new techniques of proof and adapts known proofs to make the material accessible to students with only a background in elementary real analysis. Over 60 figures are used to explain proofs, provide alternative viewpoints and elaborate on the main text. The book explains further developments in terms of measure theory. The results are presented in the context of dynamical systems, and the quantitative results are related to the underlying qualitative phenomena—chaos, randomness, recurrence and order. The final part of the book introduces and motivates measure theory and the notion of a measurable set, and describes the relationship of Birkhoff's Individual Ergodic Theorem to the preceding ideas. Developments in other dynamical systems are indicated, in particular Lévy's result on the frequency of occurence of a given digit in the partial fractions expansion of a number.
Download or read book Randomness and Recurrence in Dynamical Systems written by Rodney Nillsen and published by MAA Press. This book was released on 2010 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Randomness and Recurrence in Dynamical Systems makes accessible, at the undergraduate or beginning graduate level, results and ideas on averaging, randomness and recurrence that traditionally require measure theory. Assuming only a background in elementary calculus and real analysis, new techniques of proof have been developed, and known proofs have been adapted, to make this possible. The book connects the material with recent research, thereby bridging the gap between undergraduate teaching and current mathematical research. The various topics are unified by the concept of an abstract dynamical system, so there are close connections with what may be termed 'Probabilistic Chaos Theory' or 'Randomness'. The work is appropriate for undergraduate courses in real analysis, dynamical systems, random and chaotic phenomena and probability. It will also be suitable for readers who are interested in mathematical ideas of randomness and recurrence, but who have no measure theory background--
Download or read book Randomness and Recurrence in Dynamical Systems written by Rodney Nillsen and published by Mathematical Association of America. This book was released on 2010-11-18 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Randomness and Recurrence in Dynamical Systems makes accessible, at the undergraduate or beginning graduate level, results and ideas on averaging, randomness and recurrence that traditionally require measure theory. Assuming only a background in elementary calculus and real analysis, new techniques of proof have been developed, and known proofs have been adapted, to make this possible. The book connects the material with recent research, thereby bridging the gap between undergraduate teaching and current mathematical research. The various topics are unified by the concept of an abstract dynamical system, so there are close connections with what may be termed 'Probabilistic Chaos Theory' or 'Randomness'. The work is appropriate for undergraduate courses in real analysis, dynamical systems, random and chaotic phenomena and probability. It will also be suitable for readers who are interested in mathematical ideas of randomness and recurrence, but who have no measure theory background.
Download or read book Extremes and Recurrence in Dynamical Systems written by Valerio Lucarini and published by John Wiley & Sons. This book was released on 2016-04-25 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
Download or read book Extremes and Recurrence in Dynamical Systems written by Valerio Lucarini and published by John Wiley & Sons. This book was released on 2016-03-28 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
Download or read book Random Dynamical Systems written by Rabi Bhattacharya and published by Cambridge University Press. This book was released on 2007-01-08 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.
Download or read book Dynamical Systems and Linear Algebra written by Fritz Colonius and published by American Mathematical Society. This book was released on 2014-10-03 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix A via induced dynamical systems in ℝd and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which the time dependency of A(t) is given via skew-product flows using periodicity, or topological (chain recurrence) or ergodic properties (invariant measures). The authors develop generalizations of (real parts of) eigenvalues and eigenspaces as a starting point for a linear algebra for classes of time-varying linear systems, namely periodic, random, and perturbed (or controlled) systems. The book presents for the first time in one volume a unified approach via Lyapunov exponents to detailed proofs of Floquet theory, of the properties of the Morse spectrum, and of the multiplicative ergodic theorem for products of random matrices. The main tools, chain recurrence and Morse decompositions, as well as classical ergodic theory are introduced in a way that makes the entire material accessible for beginning graduate students.
Download or read book Dynamics and Randomness written by Alejandro Maass and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the lectures given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile from December 11th to 15th, 2000. This meeting brought together mathematicians, theoretical physicists and theoretical computer scientists, and graduate students interested in fields re lated to probability theory, ergodic theory, symbolic and topological dynam ics. We would like to express our gratitude to all the participants of the con ference and to the people who contributed to its organization. In particular, to Pierre Collet, Bernard Host and Mike Keane for their scientific advise. VVe want to thank especially the authors of each chapter for their well prepared manuscripts and the stimulating conferences they gave at Santiago. We are also indebted to our sponsors and supporting institutions, whose interest and help was essential to organize this meeting: ECOS-CONICYT, FONDAP Program in Applied Mathematics, French Cooperation, Fundacion Andes, Presidential Fellowship and Universidad de Chile. We are grateful to Ms. Gladys Cavallone for their excellent work during the preparation of the meeting as well as for the considerable task of unifying the typography of the different chapters of this book.
Download or read book Random Dynamical Systems written by Ludwig Arnold and published by . This book was released on 2014-01-15 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Unstable Singularities and Randomness written by Joseph P. Zbilut and published by Elsevier. This book was released on 2004-06-18 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, randomness and determinism have been viewed as being diametrically opposed, based on the idea that causality and determinism is complicated by “noise. Although recent research has suggested that noise can have a productive role, it still views noise as a separate entity. This work suggests that this not need to be so. In an informal presentation, instead, the problem is traced to traditional assumptions regarding dynamical equations and their need for unique solutions. If this requirement is relaxed, the equations admit for instability and stochasticity evolving from the dynamics itself. This allows for a decoupling from the “burden of the past and provides insights into concepts such as predictability, irreversibility, adaptability, creativity and multi-choice behaviour. This reformulation is especially relevant for biological and social sciences whose need for flexibility a propos of environmental demands is important to understand: this suggests that many system models are based on randomness and nondeterminism complicated with a little bit of determinism to ultimately achieve concurrent flexibility and stability. As a result, the statistical perception of reality is seen as being a more productive tool than classical determinism. The book addresses scientists of all disciplines, with special emphasis at making the ideas more accessible to scientists and students not traditionally involved in the formal mathematics of the physical sciences. The implications may be of interest also to specialists in the philosophy of science. · Presents the ideas in an informal language.· Provides tools for exploring data for singularities.
Download or read book Dynamics and Randomness II written by Alejandro Maass and published by Springer Science & Business Media. This book was released on 2004-05-31 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the lectures given at the Second Conference on Dynamics and Randomness held at the Centro de Modelamiento Matemático of the Universidad de Chile, from December 9-13, 2003. This meeting brought together mathematicians, theoretical physicists, theoretical computer scientists, and graduate students interested in fields related to probability theory, ergodic theory, symbolic and topological dynamics. The courses were on: -Some Aspects of Random Fragmentations in Continuous Times; -Metastability of Ageing in Stochastic Dynamics; -Algebraic Systems of Generating Functions and Return Probabilities for Random Walks; -Recurrent Measures and Measure Rigidity; -Stochastic Particle Approximations for Two-Dimensional Navier Stokes Equations; and -Random and Universal Metric Spaces. The intended audience for this book is Ph.D. students on Probability and Ergodic Theory as well as researchers in these areas. The particular interest of this book is the broad areas of problems that it covers. We have chosen six main topics and asked six experts to give an introductory course on the subject touching the latest advances on each problem.
Download or read book Dynamical Systems and Random Processes written by Jane Hawkins and published by American Mathematical Soc.. This book was released on 2019-09-23 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 16th Carolina Dynamics Symposium, held from April 13–15, 2018, at Agnes Scott College, Decatur, Georgia. The papers cover various topics in dynamics and randomness, including complex dynamics, ergodic theory, topological dynamics, celestial mechanics, symbolic dynamics, computational topology, random processes, and regular languages. The intent is to provide a glimpse of the richness of the field and of the common threads that tie the different specialties together.
Download or read book Random Perturbations of Dynamical Systems written by Yuri Kifer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians often face the question to which extent mathematical models describe processes of the real world. These models are derived from experimental data, hence they describe real phenomena only approximately. Thus a mathematical approach must begin with choosing properties which are not very sensitive to small changes in the model, and so may be viewed as properties of the real process. In particular, this concerns real processes which can be described by means of ordinary differential equations. By this reason different notions of stability played an important role in the qualitative theory of ordinary differential equations commonly known nowdays as the theory of dynamical systems. Since physical processes are usually affected by an enormous number of small external fluctuations whose resulting action would be natural to consider as random, the stability of dynamical systems with respect to random perturbations comes into the picture. There are differences between the study of stability properties of single trajectories, i. e. , the Lyapunov stability, and the global stability of dynamical systems. The stochastic Lyapunov stability was dealt with in Hasminskii [Has]. In this book we are concerned mainly with questions of global stability in the presence of noise which can be described as recovering parameters of dynamical systems from the study of their random perturbations. The parameters which is possible to obtain in this way can be considered as stable under random perturbations, and so having physical sense. -1- Our set up is the following.
Download or read book Random Perturbations of Dynamical Systems written by Mark I. Freidlin and published by Springer Science & Business Media. This book was released on 2012-05-31 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many notions and results presented in the previous editions of this volume have since become quite popular in applications, and many of them have been “rediscovered” in applied papers. In the present 3rd edition small changes were made to the chapters in which long-time behavior of the perturbed system is determined by large deviations. Most of these changes concern terminology. In particular, it is explained that the notion of sub-limiting distribution for a given initial point and a time scale is identical to the idea of metastability, that the stochastic resonance is a manifestation of metastability, and that the theory of this effect is a part of the large deviation theory. The reader will also find new comments on the notion of quasi-potential that the authors introduced more than forty years ago, and new references to recent papers in which the proofs of some conjectures included in previous editions have been obtained. Apart from the above mentioned changes the main innovations in the 3rd edition concern the averaging principle. A new Section on deterministic perturbations of one-degree-of-freedom systems was added in Chapter 8. It is shown there that pure deterministic perturbations of an oscillator may lead to a stochastic, in a certain sense, long-time behavior of the system, if the corresponding Hamiltonian has saddle points. The usefulness of a joint consideration of classical theory of deterministic perturbations together with stochastic perturbations is illustrated in this section. Also a new Chapter 9 has been inserted in which deterministic and stochastic perturbations of systems with many degrees of freedom are considered. Because of the resonances, stochastic regularization in this case is even more important.
Download or read book Random Perturbations of Dynamical Systems written by M. I. Freidlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.
Download or read book Random Systems and Dynamical Systems written by and published by . This book was released on 1981 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book In the Wake of Chaos written by Stephen H. Kellert and published by University of Chicago Press. This book was released on 1994-10-28 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos theory has captured scientific and popular attention. What began as the discovery of randomness in simple physical systems has become a widespread fascination with "chaotic" models of everything from business cycles to brainwaves to heart attacks. But what exactly does this explosion of new research into chaotic phenomena mean for our understanding of the world? In this timely book, Stephen Kellert takes the first sustained look at the broad intellectual and philosophical questions raised by recent advances in chaos theory—its implications for science as a source of knowledge and for the very meaning of that knowledge itself.
