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This is a sequel to my earlier question, where I asked for an example of a shift space that is mixing but not intrinsically ergodic -- that is, it has multiple measures of maximal entropy (MMEs). Ste …

The Margulis-Ruelle inequality states that measure-theoretic entropy is controlled by Lyapunov exponents; more precisely, if $f$ is a $C^{1+\alpha}$ diffeomorphism on a $d$-dimensional manifold $M$ an …

Let Σp={1,...,p}ℤ be the full shift on p symbols, and let X ⊂ Σp be a subshift -- that is, a closed σ-invariant subset, where $\sigma\colon \Sigma_p\to \Sigma_p$ is the left shift. Then σ is expansiv …

Let $X=\{1,\dots,p\}^\mathbb{N}$ be the space of sequences on a finite alphabet with a metric inducing the product topology, and let $\sigma\colon X\to X$ be the shift map. Let $\mu$ be a $\sigma$-in …

Let $X$ be a compact metric space and let $f\colon X\to X$ be a continuous expansive map. Let $\mathcal{V}$ denote the space of Hölder continuous potential functions $\phi\colon X\to \mathbb{R}$, an …

Let $X = \Sigma_p^+ = \{1,\dots,p\}^\mathbb{N}$ and let $f=\sigma\colon X\to X$ be the shift map. Let $\mathcal{M}$ be the space of Borel $f$-invariant probability measures on $X$ endowed with the we …