5 papers
Recurrence, symbolic dynamics, and wild attractors for unimodal maps
Lori Alvin, Jernej ÄinÄ
In this paper, we construct families of unimodal maps with wild Cantor attractors and study, via symbolic dynamics, the interplay between recurrence properties of the critical orbi…
Dynamics on fences
Jernej ÄinÄ, Udayan B. Darji, Benjamin Vejnar
Homeomorphisms of the Cantor set play a central role in topology, dynamical systems and descriptive set theory. In parallel, several classes of fence-like spaces - such as the hair…
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…
Generic continuous Lebesgue measure-preserving interval maps are nowhere monotone but invertible a.e
Jozef Bobok, Jernej ÄinÄ, Piotr Oprocha +1
We consider continuous maps of the interval which preserve the Lebesgue measure. Except for the identity map or $1 - \id$ all such maps have topological entropy at least …
Beyond and : A solution to the Barge Entropy Conjecture
Jan P. BoroÅski, Jernej ÄinÄ, Piotr Oprocha
We prove the entropy conjecture of M. Barge from 1989: for every there exists a pseudo-arc homeomorphism , whose topological entropy is . Until now all pseu…