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

Format:

Book

Author/Creator:

Lu, Kening, 1962- author.

Wang, Qiudong, 1962- author.

Young, L.-S. (Lai-Sang), author.

Series:

Memoirs of the American Mathematical Society ; Volume 224, Number 1054.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 224, Number 1054

Language:

English

Subjects (All):

Attractors (Mathematics).

Differential equations, Parabolic.

Periodic functions.

Physical Description:

1 online resource (85 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2012.

Language Note:

English

Summary:

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

Contents:

""Contents""; ""Chapter 1. Introduction""; ""Chapter 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""; ""Chapter 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""; ""Chapter 4. Invariant Manifolds""; ""4.1. Standardizing the Linear Part of the Unforced Equation""

""4.2. Invariant Manifolds""""4.3. Trapping Regions""; ""Chapter 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""; ""Chapter 6. Preliminary Estimates on Solutions of the Unforced Equation""; ""6.1. â?° Estimates""; ""6.2. ³ Bounds""; ""6.3. Approximate Form of Î?_{ } for Large ""; ""Chapter 7. Time- Map of Forced Equation and Derived 2-D System""; ""7.1. Approximate Form of Kick Map""

""7.2. The Map _{ } and a Derived 2-D System""""7.3. Proofs of Theorems 3.2 and 3.5""; ""7.4. Further Analytic Preparation for Theorem 2""; ""Chapter 8. Strange Attractors with SRB Measures""; ""8.1. Review of Results from [WY1] and [WY4]""; ""8.2. Proof of Theorem 3.4""; ""Chapter 9. Application: The Brusselator""; ""9.1. The Dirichlet Case""; ""9.2. The Neumann Case""; ""Appendix A. Proofs of Propositions 3.1-3.3""; ""Appendix B. Proof of Proposition 7.5""; ""B.1. Extending the Domains of and ""; ""B.2. 2-D Invariant Manifold""; ""B.3. Proof of Proposition B.5""

""Appendix C. Proofs of Proposition 8.1 and Lemma 8.2""""Bibliography""

Notes:

"Volume 224, Number 1054 (third of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1005-2