Recurrence and transience for suspension flows

Godofredo Iommi, Thomas Jordan, Michael John Todd

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)
1 Downloads (Pure)

Abstract

We study the thermodynamic formalism for suspension flows over countable
Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for regular potentials. We define the notions of recurrence and transience of a potential in this setting. We define the renewal flow, which is a symbolic model for a class of flows with diverse recurrence features. We study the corresponding thermodynamic formalism, establishing conditions for the existence of equilibrium measures and phase transitions. Applications are given to suspension flows defined over interval maps having parabolic fixed points.
Original languageEnglish
Pages (from-to)547-592
Number of pages46
JournalIsrael Journal of Mathematics
Volume209
Issue number2
Early online date3 Nov 2015
DOIs
Publication statusPublished - 2015

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