Naturally invariant measure of chaotic attractors and the conditionally invariant measure of embedded chaotic repellers

Buljan, Hrvoje and Paar, Vladimir (2002) Naturally invariant measure of chaotic attractors and the conditionally invariant measure of embedded chaotic repellers. Physical Review E, 65 (3). pp. 36218-9. ISSN 1539-3755

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Abstract

We study local and global correlations between the naturally invariant measure of a chaotic one-dimensional map f and the conditionally invariant measure of the transiently chaotic map f_H. The two maps differ only within a narrow interval H, while the two measures significantly differ within the images f^l(H), where l is smaller than some critical number l_c. We point out two different types of correlations. Typically, the critical number l_c is small. The χ^2 value, which characterizes the global discrepancy between the two measures, typically obeys a power-law dependence on the width ε of the interval H, with the exponent identical to the information dimension. If H is centered on an image of the critical point, then l_c increases indefinitely with the decrease of ε, and the χ^2 value obeys a modulated power-law dependence on ε.

Item Type: Article
Keywords: chaos, chaotic attractors, naturally invariant measure, conditionally invariant measure, chaotic repellers
Date: February 2002
Subjects: NATURAL SCIENCES > Physics
Additional Information: Copyright (2002) by the American Physical Society.
Divisions: Faculty of Science > Department of Physics
Project code: 0119250
Publisher: American Physical Society
Depositing User: Gordana Stubičan Ladešić
Date Deposited: 23 May 2014 07:38
Last Modified: 23 May 2014 07:38
URI: http://digre.pmf.unizg.hr/id/eprint/1624

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