Upper Bounds for the Hausdorff Dimension and Stratification of an Invariant Set of an Evolution System on a Hilbert Manifold
| Autor: | V. Reitmann, A. E. Malykh, A. V. Kruk |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Hilbert manifold Partial differential equation Differential equation General Mathematics 010102 general mathematics 01 natural sciences Upper and lower bounds Stratification (mathematics) Ordinary differential equation Hausdorff dimension 0103 physical sciences 0101 mathematics Invariant (mathematics) 010301 acoustics Analysis Mathematics |
| Zdroj: | Differential Equations. 53:1715-1733 |
| ISSN: | 1608-3083 0012-2661 |
| DOI: | 10.1134/s0012266117130031 |
| Popis: | We prove a generalization of the well-known Douady–Oesterle theorem on the upper bound for the Hausdorff dimension of an invariant set of a finite-dimensional mapping to the case of a smooth mapping generating a dynamical system on an infinite-dimensional Hilbert manifold. A similar estimate is given for the invariant set of a dynamical system generated by a differential equation on a Hilbert manifold. As an example, the well-known sine-Gordon equation is considered. In addition, we propose an algorithm for the Whitney stratification of semianalytic sets on finite-dimensional manifolds. |
| Databáze: | OpenAIRE |
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