Predavatelj: Domagoj Jelić

Abstract: We show that if $G$ is a topological graph, and $f$ is a continuous map, then the induced map $\tilde{f}$ acting on the hyperspace $C(G)$ of all connected subsets of $G$ by natural formula $\tilde{f}(C)=f(C)$ carries the same entropy as $f$. It is well known that this does not hold on the larger hyperspace of all compact subsets. Also, negative examples were given for the hyperspace $C(X)$ on some continua $X$, including dendrites.

Our work extends previous positive results obtained first for a much simpler case of compact interval by completely different tools.

This is joint work with Piotr Oprocha.

Predavateljica: Teja Kac

Predavatelj: Jernej Činč

Izvleček: Intervalna funkcija f na [0,1] se imenuje lokalno eventualno surjektivna (leo), če za vsako odprto množico U iz [0,1] velja, da obstaja neko naravno število n, tako da n-ta iteracija f od U pokrije celoten interval [0,1]. V diskretnih topoloških dinamičnih sistemih je leo lastnost ena izmed najstriktnejših lastnosti, ki se jo lahko zahteva in med drugim implicira tranzitivnost dinamičnega sistema.

Na tem seminarju bom govoril o pogostosti pojavljanja leo preslikav v množici funkcij, ki imajo gosto množico periodičnih točk.

Predavatelj: Iztok Banič

Predavatelj: Piotr Oprocha (AGH University of Science and Technology, Krakow, Poland)

Abstract: The pseudoarc is an intriguing continuum that was discovered by Knaster 100 years ago. While its structure is very complicated, Bing proved that from topological perspective, pseudoarc is the typical continuum to encounter in the plane.
In this talk I will present selected results connecting pseudoarc as topological object with selected properties of dynamical systems.

Predavatelj: Udayan B. Darji (University of Louisville)

Abstract: Suppose we have a continuum X and f a continuous surjection of X. In this talk we will discuss some results in which dynamics of f imply complicated structure of X as well as the inverse limit determined by (X,f). All notions will be defined. The talk will be accessible to graduate students and nonspecialists.

Predavatelj: Jan Boroński (AGH University of Science and Technology)

I will present my joint work with Sonja Štimac on classification of strange attractors. Among the many results, our work relies on the notion of mild dissipation [CP], which allows for an inverse limit description, in terms of densely branching trees [BS].

For a large family of attractors, that include those of Lozi and Henon, two strange attractors are equivalent if and only if their kneading sequences coincide, if and only if their folding patterns agree.

References:
[BC] M. Benedicks, L.A.E. Carleson, The dynamics of the Henon map, Annals of Mathematics 133 (1991), 73–169.
[BS] J. Boroński, S. Štimac, Densely branching trees as models for Henon-like and Lozi-like attractors, preprint 2021, arXiv:2104.14780
[CP] S. Crovisier, E. Pujals, Strongly dissipative surface diffeomorphisms, Commentarii Mathematici Helvetici 93 (2018), 377–400.
[MS] M. Misiurewicz, S. Štimac, Symbolic dynamics for Lozi maps, Nonlinearity 29 (2016), 3031–3046.
[WY] Wang, Q.; Young, L.-S. Strange attractors with one direction of instability. Comm. Math. Phys. 218 (2001), 1–97.

Predavatelj: Iztok Banič

Predavateljica: Teja Kac

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič

Predavatelj: Rene Gril Rogina

Predavateljica: Teja Kac

Predavateljica: Teja Kac

Predavateljica: Judy Kennedy  (Lamar University, ZDA)

Predavateljica: Sina Greenwood (Univerza v Aucklandu, Auckland, Nova Zelandija)

Povzetek: In this talk I will give a characterisation of inverse limits of continuous functions on intervals that are arcs. In addition, I will discuss inverse limits of set-valuad functions that are graphs, and in particular, arcs or circles.

Predavanje bo v prostoru 0/103 na Koroški cesti 160.

Predavatelj: Matevž Črepnjak

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS teams – za vstop v predavalnico uporabite kodo w20dsjj

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS teams – za vstop v predavalnico uporabite kodo w20dsjj

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS teams – za vstop v predavalnico uporabite kodo w20dsjj

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS teams – za vstop v predavalnico uporabite kodo w20dsjj

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS Teams – za vstop v predavalnico uporabite kodo w20dsjj

Predavateljica: Teja Kac

Predavateljica: Teja Kac

Predavateljica: Teja Kac

Predavateljica: Teja Kac

Predavateljica: Teja Kac

Predavateljica: Tina Sovič

Predavatelj: Peter Goričan

Predavatelj: Boštjan Lemež

Predavatelj: Boštjan Lemež

Predavatelj: Matevž Črepnjak

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič

Predavateljica: Teja Kac

Predavatelj: Uroš Milutinović

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič

Predavatelj: Iztok Banič

Predavateljica: Judy Kennedy (Univerza Lamar, Združene Države Amerike)

Predavateljica: Sina Greenwood (Univerza v Aucklandu, Nova Zelandija)

Povzetek: I will consider inverse limits of sequences of upper semicontinuous set-valued functions on intervals for which the graph of each bonding function is an arc. I will show how to construct any finite tree as such an inverse limit, and one for which each bonding function is one of two specified functions. I will also touch on infinite trees.

Predavatelj: Matevž Črepnjak

Predavatelj: Uroš Milutinović

Predavatelj: Uroš Milutinović