4 citations · 8 across the 10 of their papers we have counts for
12 papers
A note on the density of periodic orbits of Anosov geodesic flow in manifolds of finite volume
Nestor Nina Zarate, Sergio Romaña
In this paper, we prove that manifolds of finite volume with Anosov geodesic flow have dense periodic orbits. The same result works for conservative Anosov flows in non-compact cas…
Geometric conditions to obtain Anosov geodesic flow in non-compact manifolds
Alexander Cantoral, Sergio Romaña
Let be a complete Riemannian manifold without focal points and curvature bounded below. We prove that when the average of the sectional curvature in tangent planes along g…
Hölder continuous maps on the interval with positive metric mean dimension
Jeovanny M. Acevedo, Sergio Romaña, Raibel Arias
Fix a compact metric space with finite topological dimension. Let be the space of continuous maps on and the space of -Hölder continuous maps on …
Fractal dimensions of the Markov and Lagrange spectra near
Harold Erazo, Carlos Gustavo Moreira, Rodolfo Gutiérrez-Romo +1
The Lagrange spectrum and Markov spectrum are subsets of the real line with complicated fractal properties that appear naturally in the study of Diophan…
Density of the level sets of the metric mean dimension for homeomorphisms
Jeovanny de Jesus Muentes Acevedo, Sergio Romaña Ibarra, Raibel Arias Cantillo
Let be an -dimensional compact riemannian manifold, with . In this paper, we prove that for any , the set consisting of homeomorphisms on with lower…
On McMullen's algorithm for the Hausdorff dimension of Complex Schottky Groups
Alejandro Ucan-Puc, Sergio Romaña
We provide a generalization of the McMullen's algorithm to approximate the Hausdorff dimension of the limit set for convex-cocompact subgroups of isometries of the Complex Hyperbol…
Riemannian manifolds with Anosov geodesic flow do not have conjugate points
Ítalo Melo, Sergio Romaña
This paper establishes a significant result concerning the absence of conjugate points in certain complete Riemannian manifolds. Specifically, we demonstrate that any complete non-…
Contributions to the study of Anosov Geodesic Flows in Non-Compact Manifolds
Ítalo Melo, Sergio Romaña
In this paper we prove that if the geodesic flow of a {compact or non-compact} complete manifold without conjugate points is of the Anosov type, then the average of the integral of…
Continuity of Hausdorff Dimension Across Generic Dynamical Lagrange and Markov Spectra II
A. Cerqueira, C. G. Moreira, S. Romaña
Let be a smooth pinched negatively curved Riemannian metric on a complete surface , and let be a basic hyperbolic set of the geodesic flow of with Hausdorff di…
Some Rigidity Theorem for Anosov Geodesic Flows
Ítalo Dowell, Sergio Romaña
In this paper, we prove that if the geodesic flow of a complete manifold without conjugate points with sectional curvatures bounded below by is of Anosov type, then the cons…
A generalization of Marstrand's theorem and some geometric applications
Carlos Gustavo Moreira, Sergio Augusto Romaña Ibarra, Waliston Luiz Silva
In this paper we prove using quite elementary methods, with a combinatorial nature, two general results related to Marstrand's projection theorem in a quite general formulation ove…
Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra
Aline Cerqueira, Carlos Matheus, Carlos Gustavo Moreira
Let be a smooth area-preserving diffeomorphism of a compact surface and let be a horseshoe of with Hausdorff dimension strictly smaller than one. Given a smoo…