Coupled map lattices without cluster expansion
Gerhard Keller Carlangelo Liverani
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
Stability index, uncertainty exponent, and thermodynamic formalism for intermingled basins of chaotic attractors
Gerhard Keller

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

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