03803nam 2200625 450 991048050940332120170822144420.01-4704-1005-2(CKB)3780000000000314(EBL)3114198(SSID)ssj0000889234(PQKBManifestationID)11521353(PQKBTitleCode)TC0000889234(PQKBWorkID)10876974(PQKB)10117350(MiAaPQ)EBC3114198(PPN)195408381(EXLCZ)99378000000000031420150417h20122012 uy 0engur|n|---|||||txtccrStrange attractors for periodically forced parabolic equations /Kening Lu, Qiudong Wang, Lai-Sang YoungProvidence, Rhode Island :American Mathematical Society,2012.©20121 online resource (85 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 224, Number 1054"Volume 224, Number 1054 (third of 4 numbers)."0-8218-8484-0 Includes bibliographical references.""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. Â³ 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""Memoirs of the American Mathematical Society ;Volume 224, Number 1054.Attractors (Mathematics)Differential equations, ParabolicPeriodic functionsElectronic books.Attractors (Mathematics)Differential equations, Parabolic.Periodic functions.515/.3534Lu Kening1962-899496Wang Qiudong1962-Young L.-S(Lai-Sang),MiAaPQMiAaPQMiAaPQBOOK9910480509403321Strange attractors for periodically forced parabolic equations2009840UNINA