|
|||||
|
|
The parameterization method for invariant manifolds III: overview and applications |
|
| Authors: | Xavier Cabré |
| Affiliation: | a Institució Catalana de Recerca i Estudis Avançats (ICREA) and Universitat Politècnica de Catalunya, Departament de Matemàtica Aplicada I, Diagonal 647, 08028 Barcelona, Spain b Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain c Department of Mathematics, The University of Texas at Austin, RLM 8.100, 1 University Station C1200, Austin, TX 78712-0257, USA |
| Abstract: | We describe a method to establish existence and regularity of invariant manifolds and, at the same time to find simple maps which are conjugated to the dynamics on them. The method establishes several invariant manifold theorems. For instance, it reduces the proof of the usual stable manifold theorem near hyperbolic points to an application of the implicit function theorem in Banach spaces. We also present several other applications of the method. |
| Keywords: | Parameterization method Invariant manifolds Slow manifolds Resonances |
| 本文献已被 ScienceDirect 等数据库收录！ | |