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math.DS2026
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…
math.DS2024
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…
math.DS2024
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…