Lecture Notes in Mathematics

By: Antonio Pumarino, Angel J. Rodriguez

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Paperback | 23 May 1997

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212 Pages

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Although chaotic behaviour had often been observed numerically earlier, the first mathematical proof of the existence, with positive probability (persistence) of strange attractors was given by Benedicks and Carleson for the Henon family, at the beginning of 1990's. Later, Mora and Viana demonstrated that a strange attractor is also persistent in generic one-parameter families of diffeomorphims on a surface which unfolds homoclinic tangency. This book is about the persistence of any number of strange attractors in saddle-focus connections. The coexistence and persistence of any number of strange attractors in a simple three-dimensional scenario are proved, as well as the fact that infinitely many of them exist simultaneously.

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Non-Fiction Mathematics Applied Mathematics Chaos Theory Science Science in General History of Science Calculus & Mathematical Analysis Differential Calculus & Equations Numerical Analysis Reference, Information & Interdisciplinary Subjects Research & Information

Information theory Cybernetics & Systems Theory

Introduction	p. 1
Saddle-Focus Connections	p. 11
The Unimodal Family	p. 21
Contractive Directions	p. 53
Critical Points of the Bidimensional Map	p. 73
The Inductive Process	p. 89
The Binding Point	p. 119
The Binding Period	p. 135
The Exclusion of Parameters	p. 153
Numerical experiments	p. 191
Bibliography	p. 193
Index	p. 195
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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