New results for estimation of Hausdorff dimension

A.Y. Pogromski; H. Nijmeijer

doi:10.1109/ISCAS.2000.857071

New results for estimation of Hausdorff dimension

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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 language	English
Title of host publication	The 2000 IEEE International Symposium on Circuits and Systems, (ISCAS 2000) 28-31 May 2000, Geneva
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	236-239
Volume	1
ISBN (Print)	0-7803-5482-6
DOIs	https://doi.org/10.1109/ISCAS.2000.857071
Publication status	Published - 2000

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10.1109/ISCAS.2000.857071

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title = "New results for estimation of Hausdorff dimension",

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.",

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New results for estimation of Hausdorff dimension. / Pogromski, A.Y.; Nijmeijer, H.
The 2000 IEEE International Symposium on Circuits and Systems, (ISCAS 2000) 28-31 May 2000, Geneva. Vol. 1 Piscataway: Institute of Electrical and Electronics Engineers, 2000. p. 236-239.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - New results for estimation of Hausdorff dimension

AU - Pogromski, A.Y.

AU - Nijmeijer, H.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

U2 - 10.1109/ISCAS.2000.857071

DO - 10.1109/ISCAS.2000.857071

M3 - Conference contribution

SN - 0-7803-5482-6

VL - 1

SP - 236

EP - 239

BT - The 2000 IEEE International Symposium on Circuits and Systems, (ISCAS 2000) 28-31 May 2000, Geneva

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -

New results for estimation of Hausdorff dimension

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