Chaotic Features of Topological Dynamical Systems.
Project Goals
Our main goal in this project is to study the topological dynamics properties of homeomorphims on compact metric spaces. We are particularly interested in the chaotic properties of cw-hyperbolic homeomorphisms, pointwise dynamics , shadowing and entropy theory.
We are mainly focused on the following topics:
1- Periodic Orbits of cw-hyperbolic homeomorphisms.
2- Entropy points, sensitive points, shadowable points and expansive points.
3- Entropy theory of sensitive homeomorphims.
4- Distal-like properties.
Collaborators:
- Alexander Arbieto, Federal University of Rio de Janeiro.
- Bernardo Carvalho, Federal University of Minas Gerais.
- Juan Carlos Salcedo, Federal University of Rio de Janeiro
Research Outcome
Outcomes:
1- Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms. (joint with Bernardo Carvalho).
2- On N-Distal Homeomorphisms. Qualitative Theory of Dynamical Systems, 2023 (Joint with Juan Carlos Salcedo).
3- Positive entropy through pointwise dynamics. Proceedings of the AMS. v. 148, p. 263-271, 2019
(Joint with Alexander Arbieto)