7 papers
At most exponential growth of periodic orbits for star flows
C. A. Morales, E. Rego, X. Wen
We prove that on any closed manifold there exists a C1 open and dense subset of star flows for which the periodic orbits grow at most expo- nentially. We also explain how our metho…
Shadowing in the presence of singularities: oriented versus standard shadowing, entropy and the structure of recurrent sets
Sakshi Jain, Piotr Oprocha, Elias Rego
We study two shadowing properties for flows that differ in the allowed reparametrizations of time: oriented shadowing permits arbitrary increasing reparametrizations, whereas stand…
A trichotomy for generic sectional-hyperbolic chain-recurrent classes
Elias Rego, Kendry Vivas
The notion of sectional-hyperbolicity is a weakened form of hyperbolicity introduced for vector fields in order to understand the dynamical behavior of certain higher-dimensional s…
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…
Rescaled topological entropy
E. Rego, C. Rojas, X. Wen
We prove that to any smooth vector field of a closed manifold it can be assigned a nonnegative number called {\em rescaled topological entropy} satisfying the following properties:…
Continuum-wise hyperbolicity, periodic shadowing, and measures of maximal entropy
Bernardo Carvalho, Piotr Oprocha, Elias Rego
We prove that cw-hyperbolic homeomorphisms with jointly continuous stable/unstable holonomies satisfy the periodic shadowing property and, if they are topologically mixing, the per…
Local Shadowing Beyond Global Shadowing: Entropy and Dense Manifold Realizations
Piotr Oprocha, Elias Rego
Shadowable points were developed to cover cases in which a local shadowing mechanism survives without a global shadowing property. We show that on every compact manifold of dimensi…