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On estimates of Hausdorff dimension of invariant compact sets
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pogromskiy |
| Copyright Year | 2015 |
| Abstract | In this paper we present two approaches to estimate the Hausdorff dimension of an invariant compact set of a dynamical system: the method of characteristic exponents (estimates of KaplanYorke type) and the method of Lyapunov functions. In the first approach, using Lyapunov's first method we exploit charachteristic exponents for obtaining such estimate. A close relationship with uniform asymptotic stability is hereby established. A second bound for the Hausdorff dimension of an invariant compact set is obtained by exploiting Lyapunov's direct method and thus relies on the use of Lyapunov functions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://pure.tue.nl/ws/files/11191011/811107.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Direct method in the calculus of variations Dynamical system Estimated Hausdorff dimension Lyapunov fractal |
| Content Type | Text |
| Resource Type | Article |
