Stabilizing subshifts

Date: Tuesday 28th October, 2025

Abstract

We study equilibrium states for continuous potentials. These objects, coming from statistical physics, have a wide range of applications in dynamical systems and to other areas. In the widely studied context of Holder continuous potentials, reflecting exponentially decreasing interactions between distant particles, the equilibrium measures have full topological support. We look for regularity conditions for the potential that allow the equilibrium states to be supported on proper sub-systems. We identify a rough threshold for this behaviour in terms of summability of variations. (Joint work with Jean-René Chazottes and Tamara Kucherenko).