Chaotic dynamics in nonlinear theory / Lakshmi Burra.
2014
QA427
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Title
Chaotic dynamics in nonlinear theory / Lakshmi Burra.
Author
Burra, Lakshmi, author.
ISBN
9788132220923 (electronic book)
8132220927 (electronic book)
9788132220916
8132220927 (electronic book)
9788132220916
Published
New Delhi : Springer, [2014]
Copyright
©2014
Language
English
Description
1 online resource.
Item Number
10.1007/978-81-322-2092-3 doi
Call Number
QA427
Dewey Decimal Classification
515/.355
Summary
Using phase?plane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics. In dynamical systems, complex behavior in a map can be indicated by showing the existence of a Smale-horseshoe-like structure, either for the map itself or its iterates. This usually requires some assumptions about the map, such as a diffeomorphism and some hyperbolicity conditions. In this text, less stringent definitions of a horseshoe have been suggested so as to reproduce some geometrical features typical of the Smale horseshoe, while leaving out the hyperbolicity conditions associated with it. This leads to the study of the so-called topological horseshoes. The presence of chaos-like dynamics in a vertically driven planar pendulum, a pendulum of variable length, and in other more general related equations is also proved.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (viewed September 18, 2014).
Available in Other Form
Print version: 9788132220916
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Table of Contents
Chapter 1. Topological Considerations
Chapter 2. Topological horseshoes and coin-tossing dynamics
Chapter 3. Chaotic Dynamics in the vertically driven planar pendulum
Chapter 4. Chaos in a pendulum with variable length.
Chapter 2. Topological horseshoes and coin-tossing dynamics
Chapter 3. Chaotic Dynamics in the vertically driven planar pendulum
Chapter 4. Chaos in a pendulum with variable length.