5 papers · 1 filter
On Topological Entropy of Piecewise Smooth Vector Fields 2
Andre Amaral Antunes, Tiago Carvalho, Regis Varao
Non-smooth vector fields does not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even…
Anosov Endomorphisms on the 2-torus: Regularity of foliations and rigidity
Marisa Cantarino, Régis Varão
We provide sufficient conditions for smooth conjugacy between two Anosov endomorphisms on the 2-torus. From that, we also explore how the regularity of the stable and unstable foli…
Chain Recurrence and Positive Shadowing in Linear Dynamics
Mayara Braz Antunes, Gabriel Elias Mantovani, Régis Varão
We study shadowing and chain recurrence in the context of linear operators acting on Banach spaces or even on normed vector spaces. We show that for linear operators there is only…
There exist transitive piecewise smooth vector fields on but not robustly transitive
Rodrigo D Euzébio, Joaby S. Jucá, Régis Varão
It is well known that smooth (or continuous) vector fields cannot be topologically transitive on the sphere . Piecewise-smooth vector fields, on the other hand, may present no…
Characterization of Non-Deterministic Chaos in Two-Dimensional Non-Smooth Vector Fields
Rodrigo D. Euzébio, Pedro G. Mattos, Régis Varão
Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient…