5 papers · 1 filter
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 …
Short-range and long-range order: a transition in block-gluing behavior in Hom shifts
Silvere Gangloff, Benjamin Hellouin de Menibus, Piotr Oprocha
Hom shifts form a class of multidimensional shifts of finite type (SFT) and consist of colorings of the grid Z2 where adjacent colours must be neighbors in a fixed finite undirecte…
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…
Renormalization in Lorenz maps -- completely invariant sets and periodic orbits
Åukasz Cholewa, Piotr Oprocha
The paper deals with dynamics of expanding Lorenz maps, which appear in a natural way as Poincarè maps in geometric models of well-known Lorenz attractor. Using both analytical an…
Interval maps with dense periodicity
Jozef Bobok, Jernej ÄinÄ, Piotr Oprocha +1
We consider the class of interval maps with dense set of periodic points CP and its closure Cl(CP) equipped with the metric of uniform convergence. Besides studying basic topologic…