Dynamics of One-Dimensional Maps

  • A. N. Sharkovsky
  • S. F. Kolyada
  • A. G. Sivak
  • V. V. Fedorenko

Part of the Mathematics and Its Applications book series (MAIA, volume 407)

Table of contents

  1. Front Matter
    Pages i-ix
  2. A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak, V. V. Fedorenko
    Pages 1-34
  3. A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak, V. V. Fedorenko
    Pages 35-53
  4. A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak, V. V. Fedorenko
    Pages 55-68
  5. A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak, V. V. Fedorenko
    Pages 69-115
  6. A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak, V. V. Fedorenko
    Pages 117-159
  7. A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak, V. V. Fedorenko
    Pages 161-182
  8. A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak, V. V. Fedorenko
    Pages 183-200
  9. A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak, V. V. Fedorenko
    Pages 201-238
  10. Back Matter
    Pages 239-262

About this book

Introduction

maps whose topological entropy is equal to zero (i.e., maps that have only cyeles of pe­ 2 riods 1,2,2 , ... ) are studied in detail and elassified. Various topological aspects of the dynamics of unimodal maps are studied in Chap­ ter 5. We analyze the distinctive features of the limiting behavior of trajectories of smooth maps. In particular, for some elasses of smooth maps, we establish theorems on the number of sinks and study the problem of existence of wandering intervals. In Chapter 6, for a broad elass of maps, we prove that almost all points (with respect to the Lebesgue measure) are attracted by the same sink. Our attention is mainly focused on the problem of existence of an invariant measure absolutely continuous with respect to the Lebesgue measure. We also study the problem of Lyapunov stability of dynamical systems and determine the measures of repelling and attracting invariant sets. The problem of stability of separate trajectories under perturbations of maps and the problem of structural stability of dynamical systems as a whole are discussed in Chap­ ter 7. In Chapter 8, we study one-parameter families of maps. We analyze bifurcations of periodic trajectories and properties of the set of bifurcation values of the parameter, in­ eluding universal properties such as Feigenbaum universality.

Keywords

DEX Invariant Volume behavior boundary element method dynamical systems eXist nonlinear dynamics online stability tool

Authors and affiliations

  • A. N. Sharkovsky
    • 1
  • S. F. Kolyada
    • 1
  • A. G. Sivak
    • 1
  • V. V. Fedorenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8897-3
  • Copyright Information Springer Science+Business Media B.V. 1997
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4846-2
  • Online ISBN 978-94-015-8897-3
  • About this book
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