59 citations
- AGH University of KrakowPL17 papers
- Czech Academy of Sciences, Nuclear Physics InstituteCZ11 papers
- Czech Academy of SciencesCZ9 papers
- Czech Technical University in PragueCZ9 papers
- University of the WitwatersrandZA9 papers
- Ghent UniversityBE7 papers
- Max Planck Institute for MathematicsDE7 papers
- Palacký University OlomoucCZ6 papers
- Jagiellonian UniversityPL5 papers
- La Trobe UniversityAU5 papers
- Shantou UniversityCN5 papers
- FZU ‒ Institute of Physics of the Academy of Sciences of the Czech RepublicCZ4 papers
19 papers · 1 filter
On limit sets and equicontinuity in the hyperspace of continua in dimension one
Domagoj Jelić, Piotr Oprocha
The paper studies the structure of -limit sets of map induced on the hyperspace of all connected compact sets, by dynamical system acting on a topolog…
Continuum-wise hyperbolicity, periodic shadowing, and measures of maximal entropy
Bernardo Carvalho, Piotr Oprocha, Elias Rego
We prove that cw-hyperbolic homeomorphisms with jointly continuous stable/unstable holonomies satisfy the periodic shadowing property and, if they are topologically mixing, the per…
On recurrence and entropy in hyperspace of continua in dimension one
Domagoj Jelić, Piotr Oprocha
We show that if is a topological graph, and is continuous map, then the induced map acting on the hyperspace of all connected subsets of by natural f…
Continuous Lebesgue measure-preserving maps on one-dimensional manifolds: a survey
Jozef Bobok, Jernej Činč, Piotr Oprocha +1
We survey the current state-of-the-art about the dynamical behavior of continuous Lebesgue measure-preserving maps on one-dimensional manifolds.
An upper bound on topological entropy of the Bunimovich stadium billiard map
Jernej Činč, Serge Troubetzkoy
We show that the topological entropy of the billiard map in a Bunimovich stadium is at most log(3.49066).
Renormalization in Lorenz maps -- completely invariant sets and periodic orbits
Łukasz 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 and…