Two speakers: Zuzana Roth (Silesian University) and Samuel Roth (Silesian University).

Zuzana Roth (Silesian University) 12:00-13:00

Li-Yorke sensitivity and a conjecture of Akin and Kolyada.

Abstract: I will be presenting a family of hyperbolic non-local models for animal aggregation developed recently (Eftimie, Fetecau). I will be showing that these models possess nontrivial symmetry groups which one can use to classify the possible states of the system according to their isotropy subgroups. In particular, I will discuss the patterns appearing near a codimension two O(2) symmetric steady-state/Hopf bifurcation.

Samuel Roth (Silesian University) 13:00-14:00

On Lipschitz Constants and Entropy.

Abstract: 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-known lower bound. We show that for piecewise monotone maps, these two quantities are equal, but for countably piecewise monotone maps, the inequality can be strict. Moreover, in the transitive and Markov case, we characterize the infimum of Lipschitz constants as the exponential of the Salama entropy of a certain reverse Markov chain associated with the map. Dynamically, this number represents the exponential growth rate of the number of iterated preimages of nearly any point.