Chaotic Dynamics in Nonlinear Theory - Lakshmi Burra

Chaotic Dynamics in Nonlinear Theory

(Autor)

Buch | Softcover
104 Seiten
2016 | Softcover reprint of the original 1st ed. 2014
Springer, India, Private Ltd (Verlag)
978-81-322-3543-9 (ISBN)
74,89 inkl. MwSt
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.

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.

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.

Erscheinungsdatum
Zusatzinfo 32 Illustrations, color; 16 Illustrations, black and white; XIX, 104 p. 48 illus., 32 illus. in color.
Verlagsort New Delhi
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie Mechanik
Naturwissenschaften Physik / Astronomie Optik
Schlagworte chaotic dynamics • Linked twist mappings • Nonlinear Dynamics • Nonlinear second-order ODEs • Periodic Solutions • Time maps
ISBN-10 81-322-3543-6 / 8132235436
ISBN-13 978-81-322-3543-9 / 9788132235439
Zustand Neuware
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