## Renormalisation-induced phase transitions for unimodal maps

Dobbs, Neil
##### Description
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.
Comment: 14 pages, 2 figures. Revised following comments of referees. First page is blank
##### Keywords
Mathematics - Dynamical Systems, 37D35, 37E05