Dynamical Systems : Stability, Symbolic Dynamics, and Chaos book cover
2nd Edition

Dynamical Systems
Stability, Symbolic Dynamics, and Chaos

ISBN 9780849384950
Published November 17, 1998 by CRC Press
520 Pages

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Book Description

Several distinctive aspects make Dynamical Systems unique, including:

  • treating the subject from a mathematical perspective with the proofs of most of the results included
  • providing a careful review of background materials
  • introducing ideas through examples and at a level accessible to a beginning graduate student
  • focusing on multidimensional systems of real variables

    The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects.
  • Table of Contents

    One Dimensional Dynamics by Iteration
    Chaos and Its Measurement
    Linear Systems
    Analysis near Fixed Points and Periodic Orbits
    Hamiltonian Systems
    Bifurcation of Periodic Points
    Examples of Hyperbolic Sets and Attractors
    Measurement of Chaos in Higher Dimensions
    Global Theory of Hyperbolic Systems
    Generic Properties
    Smoothness of Stable Manifolds and Applications

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    "…was impressed with the teachability of this text and with the exercises at the end of each chapter, which seemed be nicely graded in difficulty."