Pushforward dynamics on Wasserstein spaces and measure rigidity

Douglas Finamore, André Magalhães de Sá Gomes, Christian S. Rodrigues

For an endomorphism $\varphi$ of a closed Riemannian manifold $M$, we study the pushforward action ${\varphi }_{\ast }$ on the Wasserstein space $\mathcal{P}(M)$ at a measure ${\mu }_0$ preserved by $\varphi$.…