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  3. Introduction to the Modern Theory of Dynamical Systems
  • Cited by 1741
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    • Publisher:
      Cambridge University Press
      Publication date:
      June 2012
      April 1995
      ISBN:
      9780511809187
      9780521341875
      9780521575577
      DOI:
      https://doi.org/10.1017/CBO9780511809187
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      1.27kg, 824 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      1.16kg, 824 Pages
      • Subjects:
      Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
      Series:
      Encyclopedia of Mathematics and its Applications (54)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
    Series:
    Encyclopedia of Mathematics and its Applications (54)
    Information

    Book description

    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.

    Reviews

    ‘ … there is no other treatment coming close in terms of comprehensiveness and readability … it is indispensable for anybody working on dynamical systems in almost any context, and even experts will find interesting new proofs, insights and historical references throughout the book.’

    Source: Monatshefte für Mathematik

    ‘… contains detailed discussion … presents many recent results … The text is carefully written and is accompanied by many excercises.’

    Source: European Mathematical Society Newsletter

    ‘This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline.’

    Source: L’Enseignement Mathématique

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