Abstract
The thermodynamical formalism is studied for renormalisable maps of the interval and the natural potential −t log | Df |. Multiple and indeed infinitely many phase transitions at positive t can occur for some quadratic maps. All unimodal quadratic maps with positive topological entropy exhibit a phase transition in the negative spectrum.
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Communicated by G. Gallavotti
The author was supported by the EU training network “Conformal Structures and Dynamics”.
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Dobbs, N. Renormalisation-Induced Phase Transitions for Unimodal Maps. Commun. Math. Phys. 286, 377–387 (2009). https://doi.org/10.1007/s00220-008-0656-5
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DOI: https://doi.org/10.1007/s00220-008-0656-5