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April  2017, 10(2): 313-334. doi: 10.3934/dcdss.2017015

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

 Gerhard Keller, Department Mathematik, Univ. Erlangen-Nuremberg, Cauerstr. 11, D-91058 Erlangen, Germany

Received  November 2015 Revised  November 2016 Published  January 2017

Fund Project: This work was funded by DFG grant Ke 514/8-1. It also profited from the activities of the DFG Scientific Network "Skew Product Dynamics and Multifractal Analysis" organized by Tobias Oertel-Jäger.

Skew product systems with monotone one-dimensional fibre maps driven by piecewise expanding Markov interval maps may show the phenomenon of intermingled basins [1, 5, 16, 30]. To quantify the degree of intermingledness the uncertainty exponent [23] and the stability index [29, 20] were suggested and characterized (partially). Here we present an approach to evaluate/estimate these two quantities rigorously using thermodynamic formalism for the driving Markov map.

Citation: Gerhard Keller. Stability index, uncertainty exponent, and thermodynamic formalism for intermingled basins of chaotic attractors. Discrete & Continuous Dynamical Systems - S, 2017, 10 (2) : 313-334. doi: 10.3934/dcdss.2017015
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##### References:
The critical graph $\varphi_c$ for various choices of the parameter $a$ in Example 2.3
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