Recurrence and transience for suspension flows
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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.
Iommi , G , Jordan , T & Todd , M J 2015 , ' Recurrence and transience for suspension flows ' Israel Journal of Mathematics , vol 209 , no. 2 , pp. 547-592 . DOI: 10.1007/s11856-015-1229-x
Israel Journal of Mathematics
© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at link.spinger.com / https://dx.doi.org/10.1007/s11856-015-1229-x
Funding: Proyecto Fondecyt 1110040 for funding visit to PUC-Chile and partial support from NSF grant DMS 1109587.
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