* Title : Non-unique Equilibrium Measures for Matrix Cocycles 

* Abstract : 

In this talk, we will discuss aspects of thermodynamic formalism for matrix cocycles, with a particular focus on the existence and uniqueness of equilibrium measures. Given a matrix cocycle $A$, we consider the family of potentials $\varphi_t(x)=t\log\|A(x)\|$, as $t$ ranges over the real numbers, and study how the equilibrium measures associated with these potentials depend on the parameter $t$. We present an example of a matrix cocycle for which the equilibrium measure is unique for every $t>-2$, while for $t\leq -2$ there are multiple equilibrium measures. This provides an example of a phase transition characterized by the loss of uniqueness of equilibrium measures. This is joint work with Anthony Quas.

* Zoom link : https://us06web.zoom.us/j/83600971970?pwd=r9rB6LNgccDczW3m9HZrSZmb0b5oEo.1.

- ID : 836 0097 1970 / PW : set2026