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

摘要

Skew product systems with monotone one-dimensional fibre maps driven bypiecewise expanding Markov interval maps may show the phenomenon ofintermingled basins. To quantify the degree of intermingledness the uncertaintyexponent and the stability index were suggested by various authors andcharacterized (partially). Here we present an approach to evaluate/estimatethese two quantities rigorously using thermodynamic formalism for the drivingMarkov map.