Strange attractors for periodically forced parabolic equations
Author(s)
Bibliographic Information
Strange attractors for periodically forced parabolic equations
（Memoirs of the American Mathematical Society, no. 1054）
American Mathematical Society, c2012
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Note
"July 2013, volume 224, number 1054 (third of 4 numbers)"
Includes bibliographical references (p. 83-85)
Description and Table of Contents
Description
The authors prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behaviour. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.
Table of Contents
Introduction
Basic Definitions and Facts Statement of Theorems
Invariant Manifolds
Canonical Form of Equations Around the Limit Cycle
Preliminary Estimates on Solutions of the Unforced Equation
Time-$T$ Map of Forced Equation and Derived $2$-D System
Strange Attractors with SRB Measures Application: The Brusselator
Appendix A. Proofs of Propositions 3.1-3.3
Appendix B. Proof of Proposition 7.5
Appendix C. Proofs of Proposition 8.1 and Lemma 8.2
Bibliography
by "Nielsen BookData"