Two types of estimates of Hausdorff dimension

A.Y. Pogromski; H. Nijmeijer

doi:10.1109/COC.2000.873979

Two types of estimates 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 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 language	English
Title of host publication	Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	307-310
ISBN (Print)	0-7803-6434-1
DOIs	https://doi.org/10.1109/COC.2000.873979
Publication status	Published - 2000

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10.1109/COC.2000.873979

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title = "Two types of estimates 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 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.",

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Two types of estimates of Hausdorff dimension. / Pogromski, A.Y.; Nijmeijer, H.
Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia. Piscataway: Institute of Electrical and Electronics Engineers, 2000. p. 307-310.

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

TY - GEN

T1 - Two types of estimates 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 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.

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 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.

U2 - 10.1109/COC.2000.873979

DO - 10.1109/COC.2000.873979

M3 - Conference contribution

SN - 0-7803-6434-1

SP - 307

EP - 310

BT - Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -

Two types of estimates of Hausdorff dimension

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