Two types of estimates of Hausdorff dimension

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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 the Kaplan-Yorke type) and the method of Lyapunov functions. In the first approach, using Lyapunov's first method we exploit characteristic exponents for obtaining such estimate. A close relationship with uniform asymptotic stability hereby is established. A second bound for the Hausdorff dimension is obtained by exploiting Lyapunov's direct method and thus relies on the use of certain Lyapunov functions.
Original languageEnglish
Title of host publicationControl of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages307-310
ISBN (Print)0-7803-6434-1
DOIs
Publication statusPublished - 2000

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