Chaotic Dynamics in Nonlinear Theory [electronic resource] / by Lakshmi Burra

Author: Burra, Lakshmi
Published: New Delhi : Springer India : Imprint: Springer, 2014.
Physical Description: XIX, 104 pages 48 illustrations, 32 illustrations in color : online resource
Additional Creators: SpringerLink (Online service)

Access Online

ezaccess.libraries.psu.edu

Availability

Finding items...

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.

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.

Subject(s)

ISBN

9788132220923

Digital File Characteristics

text file PDF

Note

AVAILABLE ONLINE TO AUTHORIZED PSU USERS.

Part Of

Springer eBooks

View MARC record | catkey: 13219852