Download or read book Almost Automorphic and Almost Periodic Dynamics in Skew Product Semiflows written by Wenxian Shen and published by American Mathematical Soc.. This book was released on 1998 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of almost automorphic dynamics in differential equations. By making use of techniques from abstract topological dynamics, it is shown that almost automorphy, a notion which was introduced by S. Bochner in 1955, is essential and fundamental in the qualitative study of almost periodic differential equations.

Download or read book Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces written by Toka Diagana and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses.

Download or read book Infinite Dimensional Dynamical Systems written by John Mallet-Paret and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.​

Download or read book Stability and Bifurcation Theory for Non Autonomous Differential Equations written by Anna Capietto and published by Springer. This book was released on 2012-12-14 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.

Download or read book Featured Reviews in Mathematical Reviews 1997 1999 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on 2000-05-05 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Download or read book Almost Periodic Type Functions and Ergodicity written by Zhang Chuanyi and published by Springer Science & Business Media. This book was released on 2003-06-30 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of almost periodic functions was first developed by the Danish mathematician H. Bohr during 1925-1926. Then Bohr's work was substantially extended by S. Bochner, H. Weyl, A. Besicovitch, J. Favard, J. von Neumann, V. V. Stepanov, N. N. Bogolyubov, and oth ers. Generalization of the classical theory of almost periodic functions has been taken in several directions. One direction is the broader study of functions of almost periodic type. Related this is the study of ergodic ity. It shows that the ergodicity plays an important part in the theories of function spectrum, semigroup of bounded linear operators, and dynamical systems. The purpose of this book is to develop a theory of almost pe riodic type functions and ergodicity with applications-in particular, to our interest-in the theory of differential equations, functional differen tial equations and abstract evolution equations. The author selects these topics because there have been many (excellent) books on almost periodic functions and relatively, few books on almost periodic type and ergodicity. The author also wishes to reflect new results in the book during recent years. The book consists of four chapters. In the first chapter, we present a basic theory of four almost periodic type functions. Section 1. 1 is about almost periodic functions. To make the reader easily learn the almost periodicity, we first discuss it in scalar case. After studying a classical theory for this case, we generalize it to finite dimensional vector-valued case, and finally, to Banach-valued (including Hilbert-valued) situation.

Download or read book Dynamical Systems in Population Biology written by Xiao-Qiang Zhao and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Population dynamics is an important subject in mathematical biology. A cen tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a model are periodic functions of time with commensurate period, a periodic system arises; if these periodic functions have different (minimal) periods, we get an almost periodic system. The existing reference books, from the dynamical systems point of view, mainly focus on autonomous biological systems. The book of Hess [106J is an excellent reference for periodic parabolic boundary value problems with applications to population dynamics. Since the publication of this book there have been extensive investigations on periodic, asymptotically periodic, almost periodic, and even general nonautonomous biological systems, which in turn have motivated further development of the theory of dynamical systems. In order to explain the dynamical systems approach to periodic population problems, let us consider, as an illustration, two species periodic competitive systems dUI dt = !I(t,Ul,U2), (0.

Download or read book Dynamical Systems written by S.-N. Chow and published by Springer. This book was released on 2003-12-15 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The C.I.M.E. session on Dynamical Systems, held in Cetraro (Italy), June 19-26, 2000, focused on the latest developments in several important areas in dynamical systems, with full development and historical context. The lectures of Chow and Mallet-Paret focus on the area of lattice differential systems, the lectures of Conto and Galleotti treat the classical problem of classification of orbits for two-dimensional autonomous systems with polynomial right sides, the lectures of Nussbaum focus on applications of fixed point theorems to the problem of limiting profiles for the solutions of singular perturbations of delay differential equations, and the lectures of Johnson and Mantellini deal with the existence of periodic and quasi-periodic orbits to non-autonomous systems. The volume will be of interest to researchers and graduate students working in these areas.

Download or read book Theory of Translation Closedness for Time Scales written by Chao Wang and published by Springer Nature. This book was released on 2020-05-05 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.

Download or read book Metrical Almost Periodicity and Applications to Integro Differential Equations written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-06-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamics of Evolutionary Equations written by George R. Sell and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. This book serves as an entrée for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations.

Download or read book Dynamical Systems and Their Applications in Biology written by Shigui Ruan and published by American Mathematical Soc.. This book was released on 2003-01-01 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the proceedings of the International Workshop on Dynamical Systems and their Applications in Biology held at the Canadian Coast Guard College on Cape Breton Island (Nova Scotia, Canada). It presents a broad picture of the current research surrounding applications of dynamical systems in biology, particularly in population biology. The book contains 19 papers and includes articles on the qualitative and/or numerical analysis of models involving ordinary, partial, functional, and stochastic differential equations. Applications include epidemiology, population dynamics, and physiology. The material is suitable for graduate students and research mathematicians interested in ordinary differential equations and their applications in biology. Also available by Ruan, Wolkowicz, and Wu is Differential Equations with Applications to Biology, Volume 21 in the AMS series Fields Institute Communications.

Download or read book Nonautonomous Dynamical Systems in the Life Sciences written by Peter E. Kloeden and published by Springer. This book was released on 2014-01-22 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.

Download or read book Nonautonomous Dynamics written by David N. Cheban and published by Springer Nature. This book was released on 2020-01-22 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes those topological methods (of dynamical systems) and theories that are useful in the study of different classes of nonautonomous evolutionary equations. The content is developed over six chapters, providing a thorough introduction to the techniques used in the Chapters III-VI described by Chapter I-II. The author gives a systematic treatment of the basic mathematical theory and constructive methods for Nonautonomous Dynamics. They show how these diverse topics are connected to other important parts of mathematics, including Topology, Functional Analysis and Qualitative Theory of Differential/Difference Equations. Throughout the book a nice balance is maintained between rigorous mathematics and applications (ordinary differential/difference equations, functional differential equations and partial difference equations). The primary readership includes graduate and PhD students and researchers in in the field of dynamical systems and their applications (control theory, economic dynamics, mathematical theory of climate, population dynamics, oscillation theory etc).

Download or read book Realization of Vector Fields and Dynamics of Spatially Homogeneous Parabolic Equations written by Edward Norman Dancer and published by American Mathematical Soc.. This book was released on 1999 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working in partial differential equations.

Download or read book Simplicial Dynamical Systems written by Ethan Akin and published by American Mathematical Soc.. This book was released on 1999 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: A simplicial dynamical system is a simplicial map $g: K DEGREES* \rightarrow K$ where $K$ is a finite simplicial complex triangulating a compact polyhedron $X$ and $K DEGREES*$ is a proper subdivision of $K$, for example, the barycentric or any further subdivision. the dynamics of the asociated piecewise linear map $g: X X$ can be analyzed by using certain naturally related subshifts of finite type. Any continous map on $X$ can be $C DEGREES0$ approximated by such systems. Other examples yield interesting

Download or read book The Riemann Problem for the Transportation Equations in Gas Dynamics written by Wancheng Sheng and published by American Mathematical Soc.. This book was released on 1999 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which has been merely discussed so far. The generalized Rankine-Hugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically