23 citations · 59 across the 12 of their papers we have counts for
16 papers
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…
Equilibrium states for maps isotopic to Anosov
Carlos F. Álvarez, Adriana Sánchez, Régis Varão
In this work we address the problem of existence and uniqueness (finiteness) of ergodic equilibrium states for partially hyperbolic diffeomorphisms isotopic to Anosov on $\mathbb{T…
The disintegration of measures with periodic repetitive pattern
Bruno Santiago, Régis Varão
In the context of locally constant skew-products over the shift with circle fiber maps we introduce the notion of measures with periodic repetitive pattern, inspired by \cite{GorIl…
Classification of Conditional Measures Along Certain Invariant One-Dimensional Foliations
Marcielis Espitia, Gabriel Ponce, Régis Varão
Let be a homeomorphism over a compact Riemannian manifold, ergodic with respect to a measure defined on the completion of the Borel -algebra and a $f…
A note on invariant measures for Filippov systems
Douglas Duarte Novaes, Régis Varão
We are interested in Filippov systems which preserve a probability measure on a compact manifold. We define a measure to be invariant for a Filippov system as the natural analogous…
Measure Rigidity and Disintegration: Time-one map of flows
Gabriel Ponce, Régis Varão
An invariant measure for a flow is, of course, an invariant measure for any of its time-t maps. But the converse is far from being true. Hence, one may naturally ask: What is the o…
Chaos induced by sliding phenomena in Filippov systems
Douglas Duarte Novaes, Gabriel Ponce, Régis Varão
In this paper we provide a full topological and ergodic description of the dynamics of Filippov systems nearby a sliding Shilnikov orbit. More specifically we prove that the first…
Rigidity for partially hyperbolic diffeomorphisms
Régis Varão
In this work we completely classify conjugacy for conservative partially hyperbolic diffeomorphisms homotopic to a linear Anosov automorphism on the 3-torus by its cente…
On the Bernoulli property for certain partially hyperbolic diffeomorphisms
Gabriel Ponce, Ali Tahzibi, Régis Varão
We address the classical problem of equivalence between Kolmogorov and Bernoulli property of smooth dynamical systems. In a natural class of volume preserving partially hyperbolic…
Lyapunov exponents and regularity of invariant foliations for partially hyperbolic diffeomophisms on
Regis Varao
We briefly survey some of the recent results concerning the metric behavior of the invariant foliations for a partially hyperbolic on a three-dimensional manifold and propose a con…
Mono-atomic disintegration and Lyapunov exponents for derived from Anosov diffeomorphisms
Gabriel Ponce, Régis Varão, Ali Tahzibi
In this paper we mainly address the problem of disintegration of Lebesgue measure and measure of maximal entropy along the central foliation of (conservative) Derived from Anosov (…
Center foliation: absolute continuity, disintegration and rigidity
Regis Varao
In this paper we address the issues of absolute continuity for the center foliation (as well as the disintegration on the non-absolute continuous case) and rigidity of volume prese…