An Introduction to the Theory of Smooth Dynamical Systems
Author: Wieslaw Szlenk
Publisher:
Published: 1984
Total Pages: 369
ISBN-13: 9788301037987
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An Introduction to the Theory of Smooth Dynamical Systems
Author: W. Szlenk
Publisher:
Published: 1984
Total Pages: 388
ISBN-13:
DOWNLOAD EBOOK →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.
Piecewise-smooth Dynamical Systems
Author: Mario Bernardo
Publisher: Springer Science & Business Media
Published: 2008-01-01
Total Pages: 497
ISBN-13: 1846287081
DOWNLOAD EBOOK →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.
Introduction to the Modern Theory of Dynamical Systems
Author: Anatole Katok
Publisher: Cambridge University Press
Published: 1995
Total Pages: 828
ISBN-13: 9780521575577
DOWNLOAD EBOOK →This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
Non-Smooth Dynamical Systems
Author: Markus Kunze
Publisher: Springer
Published: 2014-01-15
Total Pages: 244
ISBN-13: 9783662206102
DOWNLOAD EBOOK →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.
Smooth Dynamical Systems
Author: M. C. Irwin
Publisher: World Scientific
Published: 2001
Total Pages: 273
ISBN-13: 9810245998
DOWNLOAD EBOOK →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.
Smooth Ergodic Theory of Random Dynamical Systems
Author: Pei-Dong Liu
Publisher: Springer
Published: 2006-11-14
Total Pages: 233
ISBN-13: 3540492917
DOWNLOAD EBOOK →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.
Differential Dynamical Systems, Revised Edition
Author: James D. Meiss
Publisher: SIAM
Published: 2017-01-24
Total Pages: 392
ISBN-13: 161197464X
DOWNLOAD EBOOK →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.
Geometric Theory of Dynamical Systems
Author: J. Jr. Palis
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 208
ISBN-13: 1461257034
DOWNLOAD EBOOK →... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.
Dynamical Systems, Ergodic Theory and Applications
Author: L.A. Bunimovich
Publisher: Springer Science & Business Media
Published: 2000-04-05
Total Pages: 476
ISBN-13: 9783540663164
DOWNLOAD EBOOK →This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.
