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.
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 language | English |
|---|---|
| Pages (from-to) | 547-592 |
| Number of pages | 46 |
| Journal | Israel Journal of Mathematics |
| Volume | 209 |
| Issue number | 2 |
| Early online date | 3 Nov 2015 |
| DOIs | |
| Publication status | Published - 2015 |
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Mike Todd
- School of Mathematics and Statistics - Deputy Head of School
- Pure Mathematics - Professor
Person: Academic