Dynamical Systems: Stability, Symbolic Dynamics, and Chaos

Clark Robinson

November 17, 1998 by CRC Press
Reference - 520 Pages
ISBN 9780849384950 - CAT# 8495
Series: Studies in Advanced Mathematics

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Features

  • Presents smooth and discrete systems in a unified manner
  • Includes a proof of the existence and continuity of solutions with respect to initial conditions
  • Presents explicit formulas for various bifurcations
  • Discusses the Hénon map and the Melnikov method
  • Covers both maps and differential equations; basic material for differential equations on existence of solutions; and explicit solutions of constant coefficient linear systems
  • Summary

    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.