Equilibrium states for smooth maps

TL;DR

This paper establishes an equidistribution result for smooth maps concerning their equilibrium states and applies this to the time-one map of geodesic flows on closed Riemannian manifolds.

Contribution

It introduces a new equidistribution theorem for $C^{ abla}$ maps and demonstrates its application to geodesic flows, linking dynamical systems and geometric analysis.

Findings

Proves equidistribution for smooth maps with respect to equilibrium states.

Applies the theoretical result to geodesic flows on Riemannian manifolds.

Establishes a connection between dynamical systems and geometric structures.

Abstract

We prove an equidistribution result for $C^{\infty}$ maps with respect to equilibrium states. We apply the result to the time-one map of the geodesic flow of a closed smooth Riemannian manifold.