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

• Record Nr.: UNINA9910812533303321
• Autore: Lu Kening <1962->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2012; ©2012
• ISBN: 1-4704-1005-2
• Descrizione fisica: 1 online resource (85 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 224, Number 1054
• Disciplina: 515/.3534
• Soggetti: Attractors (Mathematics); Differential equations, Parabolic; Periodic functions
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 224, Number 1054 (third of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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""