Invertible contractions and asymptotically stable ODE´s that are not C<sup>1</sup>-linearizable
We present an example of a contraction di®eomorphism in in¯nite dimensions that is not C1-linearizable, and we construct a regular ordinary di®erential equation in a Hilbert space whose time-one map is that di®eomorphism. With this we have an example of an asymptotically stable ODE that is not C1-co...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/945 |
| Acceso en línea: | https://hdl.handle.net/2117/945 |
| Access Level: | acceso abierto |
| Palabra clave: | Partial differential equations Differential equations linearization conjugacy contraction Equacions en derivades parcials Equacions diferencials ordinàries Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions Classificació AMS::34 Ordinary differential equations::34D Stability theory Classificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spaces |
| Sumario: | We present an example of a contraction di®eomorphism in in¯nite dimensions that is not C1-linearizable, and we construct a regular ordinary di®erential equation in a Hilbert space whose time-one map is that di®eomorphism. With this we have an example of an asymptotically stable ODE that is not C1-conjugate to its linear part. |
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