On Hölder Dependence of the Parameterized Hartman—Grobman Theorem
| Autor: | Wen Meng Zhang, Xuan Lei, Peng Liu |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems Applied Mathematics General Mathematics 010102 general mathematics Mathematics::General Topology Parameterized complexity 01 natural sciences Hartman–Grobman theorem Homeomorphism 010101 applied mathematics Uniform norm Linearization Norm (mathematics) Functional space Diffeomorphism 0101 mathematics Mathematics |
| Zdroj: | Acta Mathematica Sinica, English Series. 38:137-147 |
| ISSN: | 1439-7617 1439-8516 |
| Popis: | The well-known Hartman-Grobman Theorem says that a C1 hyperbolic diffeomorphism F can be locally linearized by a homeomorphism Φ. For parameterized systems Fθ, known results show that the corresponding homeomorphisms Φθ exist uniquely in a functional space equipped with the supremum norm and depend continuously on the parameter θ. In this paper, we further extend the results to Holder dependence of Φθ on θ by Pugh’s strategy, but introducing a kind of special Holder norm instead of the usual supremum norm in the proof to control the linear parts of Fθ. This requires a new Holder linearization result for every Fθ. |
| Databáze: | OpenAIRE |
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