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

Scientific paper - Original scientific paper

• Author: Hrvoje Buljan
• Author: Vladimir Paar
• Author's institution: University of Zagreb; Faculty of Science; (Department of Physics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract (english)

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.

• Keywords (english): chaos; chaotic attractors; naturally invariant measure; conditionally invariant measure; chaotic repellers
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: Physical Review E
• Numbering: vol. 65, no. 3, pp. 036218-9
• p-ISSN: 1539-3755
• DOI: https://doi.org/10.1103/PhysRevE.65.036218
• URN:NBN: urn:nbn:hr:217:937773
• Publication: 2002
• Document URL: http://link.aps.org/doi/10.1103/PhysRevE.65.036218
• Type of resource: Text
• Access conditions: Open access
• Public note: Copyright (2002) by the American Physical Society.
• Created on: 2019-10-13 11:52:01