New results for estimation 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 estimates. A close relationship with uniform asymptotic stability 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 publicationThe 2000 IEEE International Symposium on Circuits and Systems, (ISCAS 2000) 28-31 May 2000, Geneva
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages236-239
Volume1
ISBN (Print)0-7803-5482-6
DOIs
Publication statusPublished - 2000

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