Differentiability of the pressure in non-compact spaces

Godofredo Iommi, Michael John Todd

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Abstract

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.
Original languageEnglish
Article number114634
Pages (from-to)151-177
JournalFundamenta Mathematicae
Volume259
Issue number2
Early online date28 Jul 2022
DOIs
Publication statusPublished - 2022

Keywords

  • Topological pressure
  • Countable Markov shifts
  • Compactifications

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