Yuri Lima

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math.DS2025

Uniqueness of the measure of maximal entropy for geodesic flows on surfaces

Yuri Lima, Davi Obata, Mauricio Poletti

We prove that if a geodesic flow on a closed orientable $C^{\infty}$ surface is transitive and has positive topological entropy, then it has a unique measure of maximal entropy. This…

math.DS2024

Measures of maximal entropy for non-uniformly hyperbolic maps

Yuri Lima, Davi Obata, Mauricio Poletti

For $C^{1 +}$ maps, possibly non-invertible and with singularities, we prove that each homoclinic class of an ergodic adapted hyperbolic measure carries at most one adapted hyperbol…

math.DS2024

Homoclinic classes of geodesic flows on rank 1 manifolds

Yuri Lima, Mauricio Poletti

Given a $C^{1 + β}$ flow $φ$ with positive speed on a closed smooth Riemannian manifold, we code two homoclinically related $φ$ -invariant probabilities by an irreducible countable to…