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Transience and thermodynamic formalism for infinitely branched interval maps

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Author(s)

Henk Bruin, Michael John Todd

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Abstract

We study a one-parameter family of countably piecewise linear interval maps, which, although Markov, fail the ‘large image property’. This leads to conservative as well as dissipative behaviour for different maps in the family with respect to Lebesgue. We investigate the transition between these two types, and study the associated thermodynamic formalism, describing in detail the second-order phase transitions (that is the pressure function is C1 but not C2 at the phase transition) that occur in transition to dissipativity. We also study the various natural definitions of pressure which arise here, computing these using elementary recurrence relations.
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Details

Original languageEnglish
Pages (from-to)171-194
JournalJournal of the London Mathematical Society
Volume86
Issue number1
Early online date12 Mar 2012
DOIs
Publication statusPublished - 2012

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