Differentiability of the pressure in non-compact spaces
Date
2022Metadata
Show full item recordAbstract
Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for systems defined in non-compact phase spaces, our main focus being countable Markov shifts. We produce metric compactifications of the space which allow us to prove that the pressure is differentiable on a residual set and outside an Aronszajn null set in the space of uniformly continuous functions. We establish a criterion, the so called sectorially arranged property, which implies that the pressure in the original system and in the compactification coincide. Examples showing that the compactifications can have rich boundaries, for example a Cantor set, are provided.
Citation
Iommi , G & Todd , M J 2022 , ' Differentiability of the pressure in non-compact spaces ' , Fundamenta Mathematicae , vol. 259 , no. 2 , 114634 , pp. 151-177 . https://doi.org/10.4064/fm182-3-2022
Publication
Fundamenta Mathematicae
Status
Peer reviewed
ISSN
0016-2736Type
Journal article
Description
Funding: G.I. was partially supported by Proyecto Fondecyt 1190194 and by CONICYT PIA ACT172001.Collections
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