Strange attractors for periodically forced parabolic equations

by Lu, Kening

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Title Statements

Full title :Strange attractors for periodically forced parabolic equations / Kening Lu, Qiudong Wang, Lai-Sang Young.

Edition Statements

Publication Date:©2013

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, Rhode Island
Language:eng
Publication Date:©2013

Notes

"July 2013, volume 224, number 1054 (third of 4 numbers)."

The Physical Object

Description:v, 85 pages : : illustrations ; : 25 cm.

Edition Identifiers

ISBN:9780821884843, 0821884840
oclc:ocn840937605
LC Classification:QA614.813
Dewey Decimal:515/.3534

Ch. 1 Introduction -- ch. 2 Basic Definitions and Facts -- 2.1.Sectorial Operators -- 2.2.Dynamical Systems Defined by Evolutionary Equations -- 2.3.Hopf Bifurcations -- 2.4.A Few Ideas from Dynamical Systems -- 2.5.SRB Measures -- ch. 3 Statement of Theorems -- 3.1.Setting and Standing Hypotheses -- 3.2.General Results for Periodically Forced Hopf Bifurcations -- 3.3.An Application: The Brusselator -- 3.4.Discussion of Results -- ch. 4 Invariant Manifolds -- 4.1.Standardizing the Linear Part of the Unforced Equation -- 4.2.Invariant Manifolds -- 4.3.Trapping Regions -- ch. 5 Canonical Form of Equations Around the Limit Cycle -- 5.1.Normal Form of Hopf Bifurcation -- 5.2.Blow-ups -- 5.3.Final Adjustments -- 5.4.Summary of Coordinate Transformations and Relevant Domains -- ch. 6 Preliminary Estimates on Solutions of the Unforced Equation -- 6.1.C0 Estimates -- 6.2.C3 Bounds -- 6.3.Approximate Form of t for Large t -- ch. 7 Time-T Map of Forced Equation and Derived 2-D System -- 7.1.Approximate Form of Kick Map -- 7.2.The Map FT and a Derived 2-D System -- 7.3.Proofs of Theorems 3.2 and 3.5 -- 7.4.Further Analytic Preparation for Theorem 2 -- ch. 8 Strange Attractors with SRB Measur…

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