Dynamics of One-Dimensional Maps by A.N. SharkovskyDynamics of One-Dimensional Maps by A.N. Sharkovsky

Dynamics of One-Dimensional Maps

byA.N. Sharkovsky, S.F. Kolyada, A.G. Sivak

Paperback | December 4, 2010

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The theory of one-dimensional systems is one of the most efficient tools of nonlinear dynamics, as, on the one hand, it describes one-dimensional systems fairly completely, and on the other hand exhibits all basic complicated nonlinear effects. This volume has two main goals. Firstly, it acquaints the reader with the fundamentals of the theory of one-dimensional dynamical systems. Very simple nonlinear maps with a single point of extremum, also called unimodal maps, are studied. Unimodality is found to impose hardly any restrictions on the dynamical behaviour. Secondly, it equips the reader with a comprehensive view of the problems appearing in the theory of dynamical systems and describes the methods used for their solution in the case of one-dimensional maps. Audience: This book will be of interest to researchers and postgraduate students whose work involves nonlinear dynamics.
Title:Dynamics of One-Dimensional MapsFormat:PaperbackDimensions:272 pagesPublished:December 4, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048148464

ISBN - 13:9789048148462

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Table of Contents

Introduction. 1. Fundamental Concepts of the Theory of Dynamical Systems. Typical Examples and Some Results. 2. Elements of Symbolic Dynamics. 3. Coexistence of Periodic Trajectories. 4. Simple Dynamical Systems. 5. Topological Dynamics of Unimodal Maps. 6. Metric Aspects of Dynamics. 7. Local Stability of Invariant Sets. Structural Stability of Unimodal Maps. 8. One-Parameter Families of Unimodal Maps. References. Subject Index. Notation.