7 citations · 25 across the 10 of their papers we have counts for
11 papers
Hausdorff Dimension and Flexibility for Attractors of Non-Uniformly Hyperbolic Flows
Elias Rego, Paulo Varandas
We study the Hausdorff dimension of attracting sets of three-dimensional flows whose one-dimensional quotient dynamics is non-uniformly expanding. Our main assumption is that the q…
On the Abundance of Phase Transitions in Dynamical Systems
Alexander Arbieto, Walter Britto, Elias Rego
In this work, we investigate the mechanisms that trigger phase transitions in both discrete-time and continuous-time dynamical systems. We prove a simple topological condition that…
Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms
Bernardo Carvalho, Elias Rego
We discuss different regularities on stable/unstable holonomies of cw-hyperbolic homeomorphisms and prove that if a cw-hyperbolic homeomorphism has continuous joint stable/unstable…
On the Shadowableness of Flows With Hyperbolic Singularities
Alexander Arbieto, Andrés M. López, Elias Rego +1
In this work we study the existence of singular flows satisfying shadowing-like properties. More precisely, we prove that if C1 -vector field on a closed manifold induces a chain-r…
Contributions to the Theory of Asymptotically Sectional Hyperbolic Flows
Alexander Arbieto, Miguel Pineda, Elias Rego +1
In this paper, we make several contributions to the theory of asymptotically sectional-hyperbolic (ASH) flows. First, we prove that every star ASH attractor for a vector fiel…
On Chaotic Behavior of ASH Attractors
Elias Rego, Kendry J. Vivas
The asymptotic sectional hyperbolicity is a weak notion of hyperbolicity that extends properly the sectional-hyperbolicity and includes the Rovella attractor as a archetypal exampl…
Rescaled-Expansive Flows: Unstable Sets and Topological Entropy
Alexander Arbieto, Alfonso Artigue, Elias Rego
In this work we introduce and explore a rescaled-theory of local stable and unstable sets for rescaled-expansive flows and its applications to topological entropy. We introduce a r…
Expansive Lie Group Actions
Elias Rego, Alexander Arbieto
In this work we introduce a concept of expansiveness for actions of connected Lie groups. We study some of its properties and investigate some implications of expansiveness. We stu…
On N-Distal Homeomorphisms
E. Rego, J. C. Salcedo
In this work we exploit the notion of N-distal property for a homeomorphisms. We study how it behaves under factor operations. We investigate the relation between N-distality and t…
On The Entropy of Continuous Flows With Uniformly Expansive Points and The Globalness of Shadowable Points With Gaps
Elias Rego, Alexander Arbieto
In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an e…
Positive Entropy Through Pointwise Dynamics
A. Arbieto, E. Rego
We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient cond…