2019
Jan
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# Dynamics Lunch

- 2018 Dec 18
# Dynamics Lunch: Omer Ben-Neria "Dichotomies for Borel equivalence relations"

12:00pm to 1:00pmAbstract: We would like present several results in descriptive set theory involving definable equivalence relations on Polish spaces. Given an equivalence relation E on a polish space X, we would like to study the classification problem of determining whether two objects x,y in X are E-related. - 2018 Dec 11
- 2018 Dec 04
- 2018 Nov 27
- 2018 Nov 20
- 2018 Nov 13
- 2018 Nov 06
- 2018 Oct 23
# Dynamics Lunch: Amir Algom "On \alpha \beta sets."

12:00pm to 1:00pm## Location:

Manchester faculty clubLet $\alpha, \beta$ be elements of infinite order in the circle group. A closed set K in the circle is called an \alpha \beta set if for every x\in K either x+\alpha \in K or x+\beta \in K. In 1979 Katznelson proved that there exist non-dense \alpha \beta sets, and that there exist \alpha \beta sets of arbitrarily small Hausdorff dimension. We shall discuss this result, and a more recent result of Feng and Xiong, showing that the lower box dimension of every \alpha \beta set is at least 1/2. - 2018 Jun 26
# Dynamics Lunch: Jasmin Matz (Huji) ״Distribution of periodic orbits of the horocycle flow״

12:00pm to 1:00pm## Location:

Manchester loungeAn old result of Hedlund tells us that there are no closed orbits for the horocycle flow on a compact Riemann surface M. The situation is different if M is non-compact in which case there is a one-parameter family of periodic orbits for every cusp of M. I want to talk about a result by Sarnak concerning the distribution of the such orbits in each of these families when their length goes to infinity. It turns out that these orbits become equidistributed in M and the rate of convergence can in fact be quantified in terms of spectral properties of the Eisenstein series on M.