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Strange Attractors for Periodically Forced Parabolic Equations
 
Kening Lu Brigham Young University, Provo, UT
Qiudong Wang University of Arizona, Tucson, AZ
Lai-Sang Young Courant Institute of Mathematical Sciences, New York University, NY
Strange Attractors for Periodically Forced Parabolic Equations
eBook ISBN:  978-1-4704-1005-6
Product Code:  MEMO/224/1054.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
Strange Attractors for Periodically Forced Parabolic Equations
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Strange Attractors for Periodically Forced Parabolic Equations
Kening Lu Brigham Young University, Provo, UT
Qiudong Wang University of Arizona, Tucson, AZ
Lai-Sang Young Courant Institute of Mathematical Sciences, New York University, NY
eBook ISBN:  978-1-4704-1005-6
Product Code:  MEMO/224/1054.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2242013; 85 pp
    MSC: Primary 37

    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 behavior. 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
     
     
    • Chapters
    • 1. Introduction
    • 2. Basic Definitions and Facts
    • 3. Statement of Theorems
    • 4. Invariant Manifolds
    • 5. Canonical Form of Equations Around the Limit Cycle
    • 6. Preliminary Estimates on Solutions of the Unforced Equation
    • 7. Time-$T$ Map of Forced Equation and Derived $2$-D System
    • 8. Strange Attractors with SRB Measures
    • 9. Application: The Brusselator
    • A. Proofs of Propositions 3.1-3.3
    • B. Proof of Proposition
    • C. Proofs of Proposition and Lemma
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2242013; 85 pp
MSC: Primary 37

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 behavior. 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.

  • Chapters
  • 1. Introduction
  • 2. Basic Definitions and Facts
  • 3. Statement of Theorems
  • 4. Invariant Manifolds
  • 5. Canonical Form of Equations Around the Limit Cycle
  • 6. Preliminary Estimates on Solutions of the Unforced Equation
  • 7. Time-$T$ Map of Forced Equation and Derived $2$-D System
  • 8. Strange Attractors with SRB Measures
  • 9. Application: The Brusselator
  • A. Proofs of Propositions 3.1-3.3
  • B. Proof of Proposition
  • C. Proofs of Proposition and Lemma
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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