arXiv:1510.00619 Abstract | arXiv Analytics

arXiv:1510.00619 [math.DS]Abstract References Reviews Resources

Stability index, uncertainty exponent, and thermodynamic formalism for intermingled basins of chaotic attractors

Published 2015-10-02Version 1

Skew product systems with monotone one-dimensional fibre maps driven by piecewise expanding Markov interval maps may show the phenomenon of intermingled basins. To quantify the degree of intermingledness the uncertainty exponent and the stability index were suggested by various authors and characterized (partially). Here we present an approach to evaluate/estimate these two quantities rigorously using thermodynamic formalism for the driving Markov map.

Categories: math.DS

Subjects: 37D35

Keywords: thermodynamic formalism, stability index, uncertainty exponent, intermingled basins, chaotic attractors

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