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.
Research Projects
-Dynamics of Group Actions and Foliations.
-Weak Hyperbolicity for Singular Flows.
-Topological Dynamics of Flows.
-Chaotic Properties of Topological Dynamical Systems.
-Applications of Entropy to Astrophysics.
Published and Accepted Papers
Published Papers
1- Asymptotically Expansive Homeomorphisms with the Shadowing Property. Journal of Mathematical Analysis and Applications 2024.
2- On the Number of Periodic Points for Expansive Pseudo-Groups. Chaos Solitons and Fractals. 2024. (Joint with Pablo Carrasco and Jana Rodriguez-Hertz).
3-Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms. Nonlinearity. 2024 (joint with Bernardo Carvalho).
4- On Chaotic Properties of ASH Attractors. Moscow Mathematical Journal, 2024. (Joint with Kendry Vivaz)
5- On The Shadowableness of Flows with Hyperbolic Singularities. Mathematische Annalen 2023. (with Alexander Arbieto, Andres Mauricio Lopez and Yeison Sanchez).
6- On N-Distal Homeomorphisms. Qualitative Theory of Dynamical Systems, 2023 (Joint with Juan Carlos Salcedo).
7-Expansive Lie Group Actions. Journal of Dynamical and Control Systems, 2022.
(Joint with Alexander Arbieto)
8- 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).
9- Positive entropy through pointwise dynamics. Proceedings of the AMS. v. 148, p. 263-271, 2020 (Joint with Alexander Arbieto)
To appear:
1- Rescaled Expansive Flows: Unstable Sets and topological Entropy. To appear in Topological Methods in Nonlinear Analysis 2024 (Joint with Alexander Arbieto and Alfonso Artigue)
Pre-Prints
1- Minimal Expansive Flows. 2024 submitted. (Joint with Alfonso Artigue)
2- Contributions o the Theory of ASH Flows. 2024 Submitted.
(Joint wih Alexander Arbieto, Miguel Pineda and Kendry Vivaz)
3- Triangular Maps and Sectional Anosov Flows. 2024 (with Andres Lopez) .
4- Entropy of Singular Suspensions. Arxiv 2024 (joint with Sergio Romanã) (Submitted for Publication).
In Preparation
1- Dynamical Coherence of Partially Hyperbolic Endormorphisms .(with Fernando Micena, Sankhadip Chakraborty and Raul Ures).
2- Volume Growth and Topological Entropy. (with Lin Li and Sergio Romana)
Co-Authors
1- Arbieto, Alexander. UFRJ-Brazil
2- Artigue, Alfonso. UDELAR- Uruguay
3- Carrasco, Pablo Daniel. UFMG-Brazil
4- Carvalho, Bernardo. University of Rome- Italy
5- Lopez, Andrés. UFRRJ - Brazil
6- Morales, Carlos Arnoldo. BHU- China
7- Pineda, Miguel. UFRJ- Brazil
8 - Rodriguez-Hertz, Jana. SUSTech-China
9 - Romaña, Sergio. UFRJ-Brazil
10- Salcedo, Juan Carlos. UFRJ-Brazil
11 - Sanchez, Yeison. Universidad Nacional-Colombia
12- Vivas, Kendry. Catolica del Norte- Chile
13- Wen, Xiao. BHU-China