Strange Attractors for Periodically Forced Parabolic Equations

ISBN-13: 9780821884843 / Angielski

Kening Lu;Qiudong Wang;Lai-Sang Young

Opis

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.

Spis treści

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