Research
My research interests lie on Dynamical Systems Theory and it is mainly concerned with the chaotic features of dynamical systems. In this page you can find the projects that I am working on, as well as a list of publications. Please click on the title of the project to see the details of the project.
I am glad of be creating an increasing network of collaborators spread along several countries, highlighting the social role of doing math. A list of my current collaborator can be found here.
Published and Accepted Papers
- Entropy of Singular Suspensions. Journal of Differential Equations 2025
(joint with Sergio Romanã) . - Rescaled Expansive Flows: Unstable Sets and topological Entropy. Topological Methods in Nonlinear Analysis 2025
(Joint with Alexander Arbieto and Alfonso Artigue)
- Asymptotically Expansive Homeomorphisms with the Shadowing Property. Journal of Mathematical Analysis and Applications 2024.
- On the Number of Periodic Points for Expansive Pseudo-Groups. Chaos Solitons and Fractals. 2024.
(Joint with Pablo Carrasco and Jana Rodriguez-Hertz). - Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms. Nonlinearity. 2024
(joint with Bernardo Carvalho).
- On Chaotic Properties of ASH Attractors. Moscow Mathematical Journal, 2024.
(Joint with Kendry Vivaz) - On The Shadowableness of Flows with Hyperbolic Singularities. Mathematische Annalen 2023.
(with Alexander Arbieto, Andres Mauricio Lopez and Yeison Sanchez).
- On N-Distal Homeomorphisms. Qualitative Theory of Dynamical Systems, 2023
(Joint with Juan Carlos Salcedo).
- Expansive Lie Group Actions. Journal of Dynamical and Control Systems, 2022.
(Joint with Alexander Arbieto) - On The Entropy of Continuous Flows with Uniformly Expansive Points and the Globalness of Shadowable Points with Gaps. Bull Braz Math Soc, New Series (2022)
(Joint with Alexander Arbieto).
- Positive entropy through pointwise dynamics. Proceedings of the AMS. v. 148, p. 263-271, 2020
(Joint with Alexander Arbieto)
Pre-Prints
- Robustly Shadowable Chain Recurrent Classes. 2025 submitted
(Joint with Manseob Lee, Carlos Morales and Xiao Wen) - The Homoclinic Structure of Generic Sectional-Hyperbolic Classes. 2025 submitted
(Joint with Kendry Vivas) - Entropy Flexibility of Dynamical Systems. 2025 submitted
(Joint with Alexander Arbieto and Piotr Oprocha) - On the Invariance of Expansive Measures for Flows. 2025 submitted
(Joint with Eduardo Pedrosa and Alexandre Trilles) - Rescaled Topological Entropy. 2025 submitted.
(Joint with C. Rojas and X. Wen) - Continuum-wise hyperbolicity and Periodic Orbits. 2025 submitted.
(Joint with Bernardo Carvalho and Piotr Oprocha) - Local Shadowing and Entropy for Homeomorphisms. 2025 submitted.
(Joint with Piotr Oprocha) - Triangular Maps and Sectional Anosov Flows. 2024
(with Andres Lopez).