Download or read book Dynamics Topology and Numbers written by Pieter Moree and published by American Mathematical Soc.. This book was released on 2020-02-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Download or read book Topological Dynamics written by Walter Helbig Gottschalk and published by American Mathematical Soc.. This book was released on 1955 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of Topological Dynamics written by J. de Vries and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.
Download or read book Topological Dynamics and Topological Data Analysis written by Robert L. Devaney and published by Springer Nature. This book was released on 2021-09-23 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9–11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.
Download or read book Dynamics Geometry Number Theory written by David Fisher and published by University of Chicago Press. This book was released on 2022-02-07 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--
Download or read book Dynamics and Numbers written by S. F. Koli︠a︡da and published by . This book was released on 2016 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties
Download or read book Topological and Ergodic Theory of Symbolic Dynamics written by Henk Bruin and published by American Mathematical Society. This book was released on 2022-12-21 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.
Download or read book Topological Theory of Dynamical Systems written by N. Aoki and published by Elsevier. This book was released on 1994-06-03 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments. This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book. Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.
Download or read book Topology and Dynamics of Chaos written by Christophe Letellier and published by World Scientific. This book was released on 2013 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto RAssler, Ren(r) Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical OCo not necessarily widely known OCo contributions (about the different types of chaos introduced by RAssler and not just the RAssler attractor; Gumowski and Mira's contributions in electronics; Poincar(r)'s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology,
Download or read book Explorations in Analysis Topology and Dynamics An Introduction to Abstract Mathematics written by Alejandro Uribe A. and published by American Mathematical Soc.. This book was released on 2020-05-21 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of calculus in the style of inquiry-based learning. The text guides students through the process of making mathematical ideas rigorous, from investigations and problems to definitions and proofs. The format allows for various levels of rigor as negotiated between instructor and students, and the text can be of use in a theoretically oriented calculus course or an analysis course that develops rigor gradually. Material on topology (e.g., of higher dimensional Euclidean spaces) and discrete dynamical systems can be used as excursions within a study of analysis or as a more central component of a course. The themes of bisection, iteration, and nested intervals form a common thread throughout the text. The book is intended for students who have studied some calculus and want to gain a deeper understanding of the subject through an inquiry-based approach.
Download or read book Dynamics and Numbers written by Sergiǐ Kolyada: and published by American Mathematical Soc.. This book was released on 2016-07-27 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties.
Download or read book Topological Aspects of the Dynamics of Fluids and Plasmas written by H.K. Moffatt and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers arising out of the program of the Institute for Theoretical Physics (ITP) of the University of California at Santa Bar bara, August-December 1991, on the subject "Topological Fluid Dynamics". The first group of papers cover the lectures on Knot Theory, Relaxation un der Topological Constraints, Kinematics of Stretching, and Fast Dynamo Theory presented at the initial Pedagogical Workshop of the program. The remaining papers were presented at the subsequent NATO Advanced Re search Workshop or were written during the course of the program. We wish to acknowledge the support of the NATO Science Committee in making this workshop possible. The scope of "Topological Fluid Dynamics" was defined by an earlier Symposium of the International Union of Theoretical and Applied Mechan ics (IUTAM) held in Cambridge, England in August, 1989, the Proceedings of which were published (Eds. H.K. Moffatt and A. Tsinober) by Cambridge University Press in 1990. The proposal to hold an ITP program on this sub ject emerged from that Symposium, and we are grateful to John Greene and Charlie Kennel at whose encouragement the original proposal was formu lated. Topological fluid dynamics covers a range of problems, particularly those involving vortex tubes and/or magnetic flux tubes in nearly ideal fluids, for which topological structures can be identified and to some extent quantified.
Download or read book Infinite Ergodic Theory of Numbers written by Marc Kesseböhmer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-10-10 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples. Contents: Preface Mathematical symbols Number-theoretical dynamical systems Basic ergodic theory Renewal theory and α-sum-level sets Infinite ergodic theory Applications of infinite ergodic theory Bibliography Index
Download or read book Differential Geometry and Topology written by Keith Burns and published by CRC Press. This book was released on 2005-05-27 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.
Download or read book Introduction to Topological Dynamics written by Konstantin Sergeevich Sibirskii and published by Springer. This book was released on 1975 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of differential equations originated at the end of the seventeenth century in the works of I. Newton, G. W. Leibniz and others. During the first century of its existence, this theory consisted only of isolated methods of solving certain types of differential equations; but the problem of the existence of a solution and its representability in quadratures was posed already in the second. As a result of numerous investigations it became clear that integrability in quadratures is an extremely rare phe nomenon and that the solution of many differential equations arising in applications cannot be expressed in quadratures. Also the methods of numerical integration of equations did not open the road to the general theory since these methods yield only one particular solution and this solution is obtained on a finite interval. Applications - especially the problems of celestial mechanics - required the clarification of at least the nature of the behavior of integral curves in the entire domain of their existence without integration of the equation. In this connection, at the end of the last century there arose the qualitative theory of differential equations, the creators of which one must by all rights consider to be H. Poincare and A. M. Lyapunov.
Download or read book Algebraic and Topological Dynamics written by S. F. Koli︠a︡da and published by American Mathematical Soc.. This book was released on 2005 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statisticalproperties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.
