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arXiv · 1708.03965

Robust sensitive dependence of geometric Gibbs states for analytic families of quadratic maps

Daniel Coronel·Juan Rivera-Letelier
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Abstract

For quadratic-like maps, we show a phenomenon of sensitive dependence of geometric Gibbs states: There are analytic families of quadratic-like maps for which an arbitrarily small perturbation of the parameter can have a definite effect on the low-temperature geometric Gibbs states. Furthermore, this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit sensitive dependence of geometric Gibbs states. We introduce a geometric version of the Peierls condition for contour models ensuring that the low-temperature geometric Gibbs states are concentrated near the critical orbit.

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Daniel Coronel, Juan Rivera-Letelier. 2017-08-13. Robust sensitive dependence of geometric Gibbs states for analytic families of quadratic maps. https://doi.org/10.1016/j.aim.2023.108964

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