5 problems

Evenness conjecture. The evenness of \vp^{\beta}^{\beta}^{\beta}^{\beta}^{\beta}^{\beta}^{\beta}^{\beta}^{\beta} can be derived from either the LTS condition alone or the Gibbs c…

Let a singular flow admit equilibrium states associated to Hölder continuous potentials. Equilibrium-state mixing conjecture. The techniques of Tsujii and Zhang can be adapted to s…

Morris's Bernoulli conjecture. The natural extension of every totally ergodic matrix equilibrium state for this collection of potentials has the Bernoulli property.

Moore's conjecture. If an equilibrium state associated to an irreducible tuple of matrices is ergodic but not totally ergodic with respect to $\sigma$, then it must fail to be ergo…

Let $\pi:X\to Y$ be a factor code from a shift of finite type $X$ to a sofic shift $Y$, let $\nu$ be an ergodic measure on $Y$, and consider the equilibrium states in the fiber…