New results for estimation of Hausdorff dimension

Author

Pogromsky, A.Yu. ; Nijmeijer, H.

Author_Institution

Dept. of Electr. Eng., Eindhoven Univ. of Technol., Netherlands

Volume

1

fYear

2000

fDate

2000

Firstpage

236

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

Keywords

Lyapunov methods; asymptotic stability; nonlinear dynamical systems; set theory; Hausdorff dimension; Kaplan-Yorke type estimates; Lyapunov functions; characteristic exponents; dynamical system; invariant compact set; uniform asymptotic stability; Asymptotic stability; Eigenvalues and eigenfunctions; H infinity control; Linear systems; Lyapunov method; Mechanical engineering; Stability analysis; Tellurium; Time varying systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2000. Proceedings. ISCAS 2000 Geneva. The 2000 IEEE International Symposium on

Conference_Location

Geneva

Print_ISBN

0-7803-5482-6

Type

conf

DOI

10.1109/ISCAS.2000.857071

Filename

857071