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Chaotic Dynamics in Nonlinear Theory

Authors: Burra, Lakshmi

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  • Presents a novel method to prove the existence of chaotic dynamics
  • Discusses the methods of phase-plane analysis, results from the theory of topological horseshoes and linked-twist maps
  • Proves the presence of chaos-like dynamics in a vertically driven planar pendulum (a pendulum of variable length)
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eBook $69.99
price for USA in USD (gross)
  • ISBN 978-81-322-2092-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.99
price for USA in USD
  • ISBN 978-81-322-2091-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-81-322-3543-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

LAKSHMI BURRA is associate professor of mathematics at Jawaharlal Nehru Technological University (JNTU), Hyderabad. Professor Burra has bagged two PhDs in mathematics: first from Osmania University, Hyderabad, and then from the University of Udine, Italy. She is also a postgraduate in philosophy. With a large number of research publications in leading international journals, her research topics include mathematical modeling of real-life problems such as epidemics, population dynamics, mathematical physics and climate modeling to chaotic dynamics. Some of her important results have been on oscillating population models and long-term models in climate including the link with sunspots. As well as her teaching responsibilities, Professor Burra continues to carry out research both in India and in Europe, where she has an active and ongoing collaboration. She has presented her work in invited talks in several international conferences in India, Europe and the USA. Professor Burra is married and has two sons.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-81-322-2092-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.99
price for USA in USD
  • ISBN 978-81-322-2091-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-81-322-3543-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Chaotic Dynamics in Nonlinear Theory
Authors
Copyright
2014
Publisher
Springer India
Copyright Holder
Springer India
eBook ISBN
978-81-322-2092-3
DOI
10.1007/978-81-322-2092-3
Hardcover ISBN
978-81-322-2091-6
Softcover ISBN
978-81-322-3543-9
Edition Number
1
Number of Pages
XIX, 104
Number of Illustrations
16 b/w illustrations, 32 illustrations in colour
Topics