Coexistence and Persistence of Strange Attractors / Edition 1

by Antonio Pumarino, Angel J. Rodriguez

Overview

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.

Product Details

ISBN-13:	9783540627319
Publisher:	Springer Berlin Heidelberg
Publication date:	03/15/2002
Series:	Lecture Notes in Mathematics , #1658
Edition description:	1997
Pages:	194
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Saddle-focus connections.- The unimodal family.- Contractive directions.- Critical points of the bidimensional map.- The inductive process.- The binding point.- The binding period.- The exclusion of parameters.