Recurrence and transience for suspension flows
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.
Citation
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 . https://doi.org/10.1007/s11856-015-1229-x
Publication
Israel Journal of Mathematics
Status
Peer reviewed
ISSN
0021-2172Type
Journal article
Rights
© 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
Description
Funding: Proyecto Fondecyt 1110040 for funding visit to PUC-Chile and partial support from NSF grant DMS 1109587.Collections
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