6 papers
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…
Special -limit sets in the hyperspace of continua: closedness and entropy for interval maps
Domagoj JeliÄ, Piotr Oprocha
This paper investigates the backward dynamics of hyperspace systems induced by continuous interval maps. Focusing on the hyperspace of continua, we provide a structural characteriz…
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…
On Lebesgue measure preserving Besicovitch functions
Jozef Bobok, Jernej ÄinÄ, Piotr Oprocha +1
We consider the space of all continuous interval maps preserving the Lebesgue measure . A continuous function is called Besicovitch if it do…
Entropy Flexibility of Dynamical Systems
Alexander Arbieto, Piotr Oprocha, Elias Rego
Inspired by Katok's intermediate entropy property [Inst. Hautes Ãtudes Sci. Publ. Math. 51 (1980), 137-173], we introduce and study the notion of entropy flexibility for discrete-…
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…