6 papers
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…
Robust transitivity without sectional-hyperbolicity
A. Arbieto, W. Britto, C. A. Morales +1
For any integer , we construct an -dimensional vector field exhibiting a robustly transitive singular attractor which is not sectional-hyperbolic. Nevertheless,…
Entropy Flexibility of Dynamical Systems
Alexander Arbieto, Piotr Oprocha, Elias Rego
Inspired by Katok's intermediate entropy property [Inst. Hautes Études Sci. Publ. Math. 51 (1980), 137-173], we introduce and study the notion of entropy flexibility for discrete-t…
Existence and Finiteness of equilibrium states for some Partially hyperbolic endomorphisms
Alexander Arbieto, Eric Cabezas
We establish the existence and finiteness of equilibrium states for a class of partially hyperbolic endomorphisms. In our first result, we assume that the central direction is simp…
Dense Lineable Criterion for Linear Dynamics
Alexander Arbieto, Manuel Saavedra
We study Li-Yorke chaos for sequences of continuous linear operators from an \(F\)-space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineabl…
Shadowing, topological entropy and recurrence of induced Morse-Smale diffeomorphisms
Alexander Arbieto, Jennyffer Bohorquez
Let be a Morse-Smale diffeomorphism defined on a compact and connected manifold without boundary. Let denote the hyperspace of all subcontinua of M end…