Jacob Palis

(Author)

Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in DynamicsHardcover, 30 July 1993

Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dynamics
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Part of Series
Cambridge Studies in Advanced Mathematics
Part of Series
Cambridge Studies in Advanced Mathematics (Hardcover)
Print Length
244 pages
Language
English
Publisher
Cambridge University Press
Date Published
30 Jul 1993
ISBN-10
0521390648
ISBN-13
9780521390644

Description

This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse homoclinic orbits, and a discussion of the subordinate bifurcations that accompany homoclinic bifurcations, including Hénon-like families. The core of the work is the investigation of the interplay between homoclinic tangencies and non-trivial basic sets. The fractal dimensions of these basic sets turn out to play an important role in determining which class of dynamics is prevalent near a bifurcation. The authors provide a new, more geometric proof of Newhouse's theorem on the co-existence of infinitely many periodic attractors, one of the deepest theorems in chaotic dynamics.

Product Details

Authors:
Jacob PalisFloris Takens
Book Format:
Hardcover
Date Published:
30 July 1993
Dimensions:
23.44 x 15.67 x 1.88 cm
ISBN-10:
0521390648
ISBN-13:
9780521390644
Language:
English
Location:
Cambridge
Pages:
244
Weight:
449.06 gm

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