Two types of estimates of Hausdorff dimension

Author

Pogromsky, A.Yu. ; Nijmeijer, H.

Author_Institution

Eindhoven Univ. of Technol., Netherlands

Volume

2

fYear

2000

fDate

2000

Firstpage

307

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

Keywords

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

fLanguage

English

Publisher

ieee

Conference_Titel

Control of Oscillations and Chaos, 2000. Proceedings. 2000 2nd International Conference

Conference_Location

St. Petersburg

Print_ISBN

0-7803-6434-1

Type

conf

DOI

10.1109/COC.2000.873979

Filename

873979