Renormalisation-induced phase transitions for unimodal maps

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Dobbs, Neil
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Abstract
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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
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