AbstractIn this talk, we consider some ergodic optimization problems for an expanding circle map. When the map is real analytic, we show that all optimizing measures of a real analytic potential function have zero entropy, unless the potential is cohomologous to constant. We also discuss some applications and related problems. This talk is based on a joint work with Weixiao Shen.Speaker高睿,研...
AbstractKinetic Brownian motion is a stochastic process that interpolates between the geodesic flow and Laplacian. It is also an analogue of Bismut’s hypoelliptic Laplacian. We prove the strong convergence of the spectrum of kinetic Brownian motion to the spectrum of base Laplacian for all compact Riemannian manifolds. This generalizes recent work of Kolb--Weich--Wolf on constant curvature sur...