From the 1 of 6 linked papers with an AI index.
6 papers
Effective uniqueness of the measure of maximal entropy in Ornstein's -metric
Vaughn Climenhaga, Teena Kumari
Every topologically mixing shift of finite type has a unique measure of maximal entropy. It follows from Ornstein theory that every invariant measure with entropy close to maximal…
Thermodynamic formalism for non-compact systems with expansivity and specification
Vaughn Climenhaga, Daniel J. Thompson, Tianyu Wang
The paper develops a thermodynamic formalism for continuous flows on non‑compact metric spaces, establishing criteria for the existence and uniqueness of equilibrium states with Gi…
A Nonstationary Ruelle-Perron-Frobenius Theorem
Vaughn Climenhaga, Gregory Hemenway
The Ruelle-Perron-Frobenius theorem is a powerful tool in the study of equilibrium measures and their statistical properties. We prove a nonstationary version of this theorem under…
Every finite horizon Sinai billiard map has a unique measure of maximal entropy
Vaughn Climenhaga, Jason Day
Finite horizon Sinai billiard maps are examples of uniformly hyperbolic systems with singularities. These discontinuities make it more difficult to develop the classical theory of…
Maximizing entropy for power-free languages
Vaughn Climenhaga
A power-free language is characterized by the number of symbols used and a limit on how many times a block of symbols can repeat consecutively. For certain values of these paramete…
Gibbs measures have local product structure
Vaughn Climenhaga
It is well-known that equilibrium measures for uniformly hyperbolic dynamical systems have a local product structure, which plays an important role in their mixing properties. Exis…