Measure rigidity for regular polynomial endomorphisms of $\mathbb C^k$ and applications

par YuGang Zhang

vendredi 6 nov. 2026, 10:30 → 12:30 Europe/Paris

A polynomial endomorphism $f$ of $\mathbb C^k$ is regular if it can be holomorphically extended to $\mathbb P^k$. For $f$ of degree at least two, its equilibrium measure is the unique invariant probability measure of maximal entropy. In this talk, we study what happens when two such maps $f$ and $g$ have the same equilibrium measure. This question is interesting in its own right and also has several applications. In particular, our measure rigidity results give a simple way to extend some other results previously known only in dimension one to dimension two.