Topological Dynamics of Flows
Project Goals
Our main goal in this project is to study the topological dynamics properties of continuous flows on compact metric spaces. We are particularly interested in the chaotic properties, expansive theory, shadowing and entropy theory of continuous flows.
We are mainly focused on the following topics:
1- Topological Entropy of Expansive singular Flows.
2- Shadowing for Singular Flows.
3- Pointwise dynamics of singular flows
4- Expansiveness of continuous flows.
Collaborators:
- Alexander Arbieto, Federal University of Rio de Janeiro
- Alfonso Artigue, University of Republic (Uruguay)
- Andres Lopez, Rural Federal University of Rio de Janeiro
- Yeison Sanchez, National University of Colombia
Research Outcome
Outcomes:
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)
2- 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).