12 citations · 21 across the 6 of their papers we have counts for
16 papers
Spaces where all closed sets are -limit sets
Jana Hantáková, Samuel Roth, Ľubomír Snoha
Metrizable spaces are studied in which every closed set is an -limit set for some continuous map and some point. It is shown that this property is enjoyed by every space contain…
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…
On backward attractors of interval maps
Jana Hantáková, Samuel Roth
Special -limit sets (-limit sets) combine together all accumulation points of all backward orbit branches of a point under a noninvertible map. The most important questi…
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 --…
Inequalities for Entropy, Hausdorff Dimension, and Lipschitz Constants
Samuel Roth, Zuzana Roth
We construct suitable metrics for two classes of topological dynamical systems (linear maps on the torus and non-invertible expansive maps on compact spaces) in order to get a lowe…
Constant slope, entropy and horseshoes for a map on a tame graph
Adam Bartoš, Jozef Bobok, Pavel Pyrih +2
We study continuous countably (strictly) monotone maps defined on a tame graph, i.e., a special Peano continuum for which the set containing branchpoints and endpoints has a counta…
Constant Slope Models and Perturbation
Michal Malek, Samuel Roth
We sharpen an estimate for the growth rate of preimages of a point under a transitive piecewise monotone interval map. Then we apply our estimate to study the continuity of the ope…
Constant Slope Models for Finitely Generated Maps
Samuel Roth
We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbat…
The Infimum of Lipschitz Constants in the Conjugacy Class of an Interval Map
Jozef Bobok, Samuel Roth
How can we interpret the infimum of Lipschitz constants in a conjugacy class of interval maps? For positive entropy maps, the exponential of the topological entropy gives a well-kn…
Constant Slope Maps on the Extended Real Line
Michał Misiurewicz, Samuel Roth
For a transitive countably piecewise monotone Markov interval map we consider the question whether there exists a conjugate map of constant slope. The answer varies depending on wh…
On the weakest version of distributional chaos
Jana Hantáková, Samuel Roth, Zuzana Roth
The aim of the paper is to correct and improve some results concerning distributional chaos of type 3. We show that in a general compact metric space, distributional chaos of type…
No Semiconjugacy to a Map of Constant Slope
Michał Misiurewicz, Samuel Roth
We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a…