Renormalisation-induced phase transitions for unimodal maps

Details Renormalisation-induced phase transitions for unimodal maps Renormalisation-induced phase transitions for unimodal maps

2007-12-18

arxiv.org/abs/0712.3023v2

Commun. Math. Phys. 286, 377\^a?"387 (2009)

Mathematics

Dynamical Systems

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

Scientific paper

10.1007/s00220-008-0656-5

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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