Weak Hyperbolicity for Flows
Project Goals
Our main goal in this project is to study the dynamical properties of singular flows with some weaker hyperbolic behavior on closed manifolds. We are particularly interested in the chaotic properties of sectional hyperbolic sets and more generally asymptotically sectional hyperbolic sets.
We are mainly focused on the following topics:
1- Entropy Theory of ASH attractors
2- Metric Properties of ASH attractors
3- Expansive Properties of ASH Attractors
Collaborators:
- Alexander Arbieto, Federal University of Rio de Janeiro
- Kendry Vivaz, Catholic University of Valparaiso.
- Andres Lopez, Rural Federal University of Rio de Janeiro
- Yeison Sanchez, National University of Colombia
- Miguel Pineda, Federal University of Rio de Janeiro
Research Outcome
Outcomes:
1- On Chaotic Properties of ASH Attractors. Moscow Mathematical Journal, 2024. (Joint with Kendry Vivaz)
2- On The Shadowableness of Flows with Hyperbolic Singularities. Mathematische Annalen 2023. (with Alexander Arbieto, Andres Mauricio Lopez and Yeison Sanchez).
In Preparation:
1- Triangular Maps for Secctional-Anosov Flows. (With Andres Lopez) .
2- Entropy Theory of ASH attractors.
(with Alexander Arbieto, Miguel Pineda and Kendry Vivaz)