Smooth Dynamical Systems

Author : Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 55,8 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9781846287084

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Piecewise-smooth Dynamical Systems by Mario Bernardo,Chris Budd,Alan Richard Champneys,Piotr Kowalczyk Pdf

This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Author : Markus Kunze
Publisher : Springer
Page : 244 pages
File Size : 50,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662206102

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Non-Smooth Dynamical Systems by Markus Kunze Pdf

The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.

Author : Michael Charles Irwin
Publisher : World Scientific
Page : 280 pages
File Size : 52,7 Mb
Release : 2001
Category : Mathematics
ISBN : 9812810129

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Smooth Dynamical Systems by Michael Charles Irwin Pdf

This is a reprint of M C Irwin''s beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area. Request Inspection Copy. Contents: Some Simple Examples; Equivalent Systems; Integration of Vector Fields; Linear Systems, Linearization, Stable Manifolds; Stable Systems; Appendices. Readership: Graduate students in mathematics.

Author : Pei-Dong Liu,Min Qian
Publisher : Springer
Page : 233 pages
File Size : 47,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540492917

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Smooth Ergodic Theory of Random Dynamical Systems by Pei-Dong Liu,Min Qian Pdf

This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

Author : M. C. Irwin
Publisher : Unknown
Page : 0 pages
File Size : 42,8 Mb
Release : 1980
Category : Differentiable dynamical systems
ISBN : OCLC:472104072

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Smooth Dynamical Systems by M. C. Irwin Pdf

Author : W. Szlenk
Publisher : Unknown
Page : 388 pages
File Size : 42,6 Mb
Release : 1984
Category : Mathematics
ISBN : UOM:39015015607313

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An Introduction to the Theory of Smooth Dynamical Systems by W. Szlenk Pdf

This book is aimed at readers who are familiar with a standard undergraduate course of mathematics. It forms a short account of the main ideas and results in the theory of smooth dynamical systems.

Author : Ludwig Arnold
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 50,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662128787

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Random Dynamical Systems by Ludwig Arnold Pdf

The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Author : Remco I. Leine,Henk Nijmeijer
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 40,8 Mb
Release : 2013-03-19
Category : Mathematics
ISBN : 9783540443988

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Dynamics and Bifurcations of Non-Smooth Mechanical Systems by Remco I. Leine,Henk Nijmeijer Pdf

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Author : Vincent Acary,Bernard Brogliato
Publisher : Springer Science & Business Media
Page : 529 pages
File Size : 45,6 Mb
Release : 2008-01-30
Category : Technology & Engineering
ISBN : 9783540753926

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Numerical Methods for Nonsmooth Dynamical Systems by Vincent Acary,Bernard Brogliato Pdf

This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.

Author : James D. Meiss
Publisher : SIAM
Page : 392 pages
File Size : 49,7 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9781611974645

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Differential Dynamical Systems, Revised Edition by James D. Meiss Pdf

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 199 pages
File Size : 40,9 Mb
Release : 2005-11-24
Category : Science
ISBN : 9783540288893

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Dynamical Systems by Jürgen Jost Pdf

Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata

Author : D.V. Anosov,V.I. Arnold,S.Kh. Aranson,I.U. Bronshtein,V.Z. Grines,Yu.S. Ilyashenko
Publisher : Springer
Page : 237 pages
File Size : 45,9 Mb
Release : 1994-06-01
Category : Mathematics
ISBN : 3540170006

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Dynamical Systems I by D.V. Anosov,V.I. Arnold,S.Kh. Aranson,I.U. Bronshtein,V.Z. Grines,Yu.S. Ilyashenko Pdf

From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." Journal de Physique

Author : Viacheslav Z. Grines,Timur V. Medvedev,Olga V. Pochinka
Publisher : Springer
Page : 295 pages
File Size : 51,9 Mb
Release : 2016-11-11
Category : Mathematics
ISBN : 9783319448473

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Dynamical Systems on 2- and 3-Manifolds by Viacheslav Z. Grines,Timur V. Medvedev,Olga V. Pochinka Pdf

This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed.“br> The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.

Author : Wieslaw Szlenk
Publisher : Unknown
Page : 369 pages
File Size : 44,8 Mb
Release : 1984
Category : Electronic
ISBN : 8301037989

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An Introduction to the Theory of Smooth Dynamical Systems by Wieslaw Szlenk Pdf

Author : Vadim Kaloshin,Ke Zhang
Publisher : Princeton University Press
Page : 218 pages
File Size : 55,5 Mb
Release : 2020-11-03
Category : Mathematics
ISBN : 9780691202525

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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom by Vadim Kaloshin,Ke Zhang Pdf

The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.