The K-property of equilibrium states for systems with non-uniform structure
Abstract
In this paper, we develop a general criterion for the K-property of equilibrium states within the Climenhaga-Thompson framework. Under suitable pressure-gap and non-uniform expansiveness assumptions, we show that the unique equilibrium state has the K-property, provided that the good collection of orbit segments satisfies an appropriate non-uniform specification property, as well as an appropriate non-uniform distortion control property for the potential function. These results do not require any additional lambda-decomposition structure and apply to a wide range of systems, including those with non-trivial central directions, such as the frame flow over closed rank-one manifolds with bunched nonpositive curvature. Moreover, we also construct several counterexamples to demonstrate that generally the assumptions in our criteria cannot be weakened while keeping the K-property.
Related
- Uniform Embeddings of Banach Space Spheres into Hilbert Spaces and Property (H)
- The Uniform Primary Factorisation Property for C(K,E)
- The uniform-in-time electrostatic limit of the linearised Vlasov-Maxwell system: the Poisson equilibrium
- Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution
- Generic Sharp Shift Embedding for Amenable Group Actions with the Uniform Rokhlin Property and Comparison
BibTeX
@misc{wang2026kproperty,
title = {{The K-property of equilibrium states for systems with non-uniform structure}},
author = {Tianyu Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37392},
eprint = {2610.37392},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37392},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The K-property of equilibrium states for systems with non-uniform structure
AU - Tianyu Wang
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37392
UR - https://arxiv.org/abs/2610.37392
AB - In this paper, we develop a general criterion for the K-property of equilibrium states within the Climenhaga-Thompson framework. Under suitable pressure-gap and non-uniform expansiveness assumptions, we show that the unique equilibrium state has the K-property, provided that the good collection of orbit segments satisfies an appropriate non-uniform specification property, as well as an appropriate non-uniform distortion control property for the potential function. These results do not require any additional lambda-decomposition structure and apply to a wide range of systems, including those with non-trivial central directions, such as the frame flow over closed rank-one manifolds with bunched nonpositive curvature. Moreover, we also construct several counterexamples to demonstrate that generally the assumptions in our criteria cannot be weakened while keeping the K-property.
ER -