2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220077The 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 blankDynamical Systems37D35; 37E05text