On maximizing measures of homeomorphisms on compact manifolds

We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g : X -> R, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral integral(X) g d mu, considered as a function on the space of all T-invariant Borel probability measures mu, attains its maximum on a measure supported on a periodic orbit.

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq[301485/03-8]

CNPq[304360/05-8]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)