One-Dimensional Dynamics and High-Dimensional Network Systems

A counterexample to Hölder regularity of the stationary measure for random noninvertible maps.

Not scheduled

25m

Aula Dini (Palazzo del Castelletto)

Short Talk

Speaker

Vincent Goverse (Imperial College London)

Description

Gorodetski, Kleptsyn, and Monakov [1] recently proved that for random dynamical systems on compact Riemannian manifolds generated by bi-Lipschitz homeomorphisms, the stationary measure is Hölder regular whenever the maps do not share a common invariant measure. In this talk, we show that this result does not extend to noninvertible, locally Lipschitz maps. We construct an explicit one-dimensional counterexample in which the stationary physical measure of such a system fails to be Hölder regular.
Joint work with V. Kleptsyn.

[1] A. Gorodetski, V. Kleptsyn, and G. Monakov, Hölder regularity of stationary measures, Invent. Math. 243 (2026), 1037–1077.