PMID: 11909223Mar 23, 2002Paper

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Hrvoje Buljan, Vladimir Paar

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 chi(2) value, which characterizes the global discrepancy between the two measures, typically obeys a power-law dependence on the width epsilon 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 epsilon, and the chi(2) value obeys a modulated power-law dependence on epsilon.

References

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Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·V Paar, H Buljan
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·H Buljan, V Paar
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M Dhamala, Y C Lai
Jun 5, 2003·Chaos·Milos Dolnik, Erik M. Bollt

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