On estimates of Hausdorff dimension of invariant compact sets
نویسندگان
چکیده
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.
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