Program v akademickém roce 2024/2025
5. 3. 2025
Piotr Oprocha (AGH University of Kraków), Tracing properties and topological structure of invariant measures.
Abstract: In 1970s Bowen related hyperbolic dynamics with specification property and used this to show that there exists a unique measure of maximal entropy. Almost the same time Sigmund used specification property as a tool in characterization of simplex of invariant measures. Since then, these results were inspiration for numerous mathematicians in various studies of dynamics. Several weaker versions of specification property were developed and used as a tool for better understanding of dynamics. At the same time, questions, how often such properties can be found in dynamics were raised (e.g. in the sense of Baire category theorem).
In this talk we will present selected questions and results fitting into the above framework of research.
26. 2. 2025
Dario Darji (Matematicko-fyzikální fakulta, Univerzita Karlova), Shadowing in Hyperspace.
Abstract: What is the shadowing property for maps defined on a manifold or a compact metric space in general?
Why is it relevant? Does the shadowing property of a dynamical system implies “collection wise” shadowing? Come find out.
19. 2. 2025
Dra. Verónica Martínez de la Vega y Mansilla (Instituto de Matemáticas, UNAM), Open Selections on dendroids.
Abstract: A continuum is a compact connected metric space; a dendroid is an arcwise hereditary unicoherent continuum. Given a continuum X, we denote by
2X = { A ⊂ X : A is closed and A ≠ ∅ },
C(X) = { A ∈ 2X : A is connected}.
A selection is a continuous map s : C(X) → X satisfying that s(A) ∈ A, A ∈ C(X).
In this talk will go carefully through the above definitions and we will give several examples, then we will be able to define open selections by solving the problem of how to send open maps from n-cells to trees.
A 2-cell is the space [0,1] x [0,1] in general an n-cell is the space [0,1] x [0,1] … [0,1] (n times); an open map is a continuous function that sends open sets into open sets, and a tree is the union of intervals that intersect only at its end points and do not have cycles.
In this talk we show a way of constructing open maps from n-cells onto trees. The construction of these maps are very geometrical and only the notion of map and open set is needed to understand the main construction of this talk.
18. 12. 2024
Lukáš Václavík, O Sarnakově domněnce,
Rostislav Klech, Topologická entropie na slabě souvislých grafech,
Michaela Záškolná, Fraktálové dimenze a jejich využití,
Veronika Rýžová, On one of Birkhoff’s theorems for backward limit points.
4. 12. 2024
Matěj Moravík, Some properties regarding asymptotic pairs in positive entropy dynamical systems.
27. 11. 2024
Jana Hantáková a Michaela Mlíchová, Charakterizace Milnorových atraktorů v 1 a 2 dimenzionálních prostorech.
16. 10. 2024
Michal Málek, Má smysl tranzitivita u neautonomních dynamických systémů? Hledání vhodné definice.
Seminař se koná zpravidla každý lichý týden ve středu od 13:05 do 14:40 v učebně R1.
