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PreprintarXiv licencearXiv

Thermodynamic formalism for non-compact systems with expansivity and specification

  • Vaughn Climenhaga
  • Daniel J. Thompson
  • Tianyu Wang
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Abstract

We develop a new theory of thermodynamic formalism for non-compact flows, providing criteria for existence and uniqueness of equilibrium states, as well as ergodicity and a Gibbs property. These criteria include new versions of the expansivity and specification properties that hold for geodesic flows on non-compact negatively curved manifolds. Previous results on thermodynamic formalism for these geodesic flows were restricted by a pinched curvature condition, which we remove, allowing curvature to approach both $0$ and −∞. Our results also apply to geodesic flows beyond the smooth setting, including locally CAT(-1) spaces.

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Cite

BibTeXRIS
BibTeX
@misc{climenhaga2026thermodynamic,
  title = {{Thermodynamic formalism for non-compact systems with expansivity and specification}},
  author = {Vaughn Climenhaga and Daniel J. Thompson and Tianyu Wang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2606.20405},
  eprint = {2606.20405},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.20405},
}
RIS
TY  - UNPB
TI  - Thermodynamic formalism for non-compact systems with expansivity and specification
AU  - Vaughn Climenhaga
AU  - Daniel J. Thompson
AU  - Tianyu Wang
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2606.20405
UR  - https://arxiv.org/abs/2606.20405
AB  - We develop a new theory of thermodynamic formalism for non-compact flows, providing criteria for existence and uniqueness of equilibrium states, as well as ergodicity and a Gibbs property. These criteria include new versions of the expansivity and specification properties that hold for geodesic flows on non-compact negatively curved manifolds. Previous results on thermodynamic formalism for these geodesic flows were restricted by a pinched curvature condition, which we remove, allowing curvature to approach both $0$ and −∞. Our results also apply to geodesic flows beyond the smooth setting, including locally CAT(-1) spaces.
ER  -