Renormalisation-induced phase transitions for unimodal maps

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.

14 pages, 2 figures. Revised following comments of referees. First page is blank