Yuri Lima

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math.DS2025

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.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

Homoclinic classes of geodesic flows on rank 1 manifolds

Yuri Lima, Mauricio Poletti

Given a $C^{1 + I^^{2}}$ flow $I ¨ $ with positive speed on a closed smooth Riemannian manifold, we code two homoclinically related $I ¨ $ -invariant probabilities by an irreducible countable…