Renormalisation-Induced Phase Transitions for Unimodal Maps

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. The author was supported by the EU training network “Conformal Structures and Dynamics”.