4 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 Jelić, 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…
On Lebesgue measure preserving Besicovitch functions
Jozef Bobok, Jernej Činč, Piotr Oprocha +1
We consider the space of all continuous interval maps preserving the Lebesgue measure . A continuous function is called Besicovitch if it does…
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…