8 papers
Rigidity and Flexibility of Polynomial Entropy
Samuel Roth, Zuzana Roth, Ľubomír Snoha
We introduce the notion of a one-way horseshoe and show that the polynomial entropy of an interval map is given by one-way horseshoes of iterates of the map, obtaining in such a wa…
Dendrites and measures with discrete spectrum
Magdalena Foryś-Krawiec, Jana Hantáková, Jiří Kupka +2
We are interested in dendrites for which all invariant measures of zero-entropy mappings have discrete spectrum, and we prove that this holds when the closure of the endpoint set o…
Typical behaviour of random interval homeomorphisms
Jaroslav Bradík, Samuel Roth
We consider the typical behaviour of random dynamical systems of order-preserving interval homeomorphisms with a positive Lyapunov exponent condition at the endpoints. Our study re…
A non-Borel special alpha-limit set in the square
Steve Jackson, Bill Mance, Samuel Roth
We consider the complexity of special -limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necess…
Dynamics on dendrites with closed endpoint sets
Samuel Roth
We construct dendrites with endpoint sets isometric to any totally disconnected compact metric space. This allows us to embed zero-dimensional dynamical systems into dendrites and…
Fair Measures for Countable-to-one Maps
Ana Rodrigues, Samuel Roth, Zuzana Roth
In this paper we generalize the recently introduced concept of fair measure (M. Misiurewicz and A. Rodrigues, Counting preimages. Ergod. Th. & Dynam. Sys. 38 (2018), no. 5, 1837 --…