Let $T:X\to X$ be an expansive continuous map on a compact [metric space](/page/Metric%20Space) with specification. Let $\phi:X\to\mathbb R$ be continuous and have the Bowen property. Then $\phi$ has a unique equilibrium state. This measure is Gibbs at sufficiently small Bowen scales.
Knowledge Status
Analysis
Discussion
States and proves Bowen Uniqueness Theorem for Equilibrium States, a result in advanced ergodic theory focused on entropy, dynamical structure, and related invariants.