Robust sensitive dependence of geometric Gibbs states for analytic families of quadratic maps
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Date
2023
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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. (c) 2023 Elsevier Inc. All rights reserved.
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Sensitive dependence of Geometric, Gibbs states, Quadratic-like