Abstract Consider a compact surface of genus $\geq 2$ equipped with metric that is flat everywhere except at finitely many cone points angles greater than $2\pi $. Following the technique in work Burns, Climenhaga, Fisher, and Thompson, we prove sufficiently regular potential functions have unique equilibrium states if singular set does not support full pressure. Moreover, show pressure gap hol...

Hofer’s metric is a very interesting way of measuring distances between compactly supported Hamiltonian symplectic maps. Unfortunately, it is not known yet how to compute it in general, for example for symplectic maps far away from each other. It is known that Hofer’s metric is locally flat, and it can be computed by the so-called oscillation norm of the difference between the Poincare generati...