Stability index, uncertainty exponent, and thermodynamic formalism for intermingled basins of chaotic attractors
Gerhard Keller
Discrete & Continuous Dynamical Systems - S 2017, 10(2): 313-334 doi: 10.3934/dcdss.2017015

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.

keywords: Intermingled basins chaotic attractors skew product system stability index uncertainty exponent thermodynamic formalism large deviations
Coupled map lattices without cluster expansion
Gerhard Keller Carlangelo Liverani
Discrete & Continuous Dynamical Systems - A 2004, 11(2&3): 325-335 doi: 10.3934/dcds.2004.11.325
We present an approach to the investigation of the statistical properties of weakly coupled map lattices that avoids completely cluster expansion techniques. Although here it is implemented on a simple case we expect similar strategies to be applicable in a much larger class of situations.
keywords: Coupled map lattice exponential decay of correlations transfer operator spatio-temporal chaos. spectral gap

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