Low-temperature phase transitions in the quadratic family
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Date
2013
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Abstract
We give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function. This implies that several dimension spectra and large deviation rate functions associated to this map are not (expected to be) real analytic, in contrast to the uniformly hyperbolic case. The quadratic map we study has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense. (c) 2013 Elsevier Inc. All rights reserved.
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Keywords
Quadratic family, Thermodynamic formalism