Events & Seminars

2016 Nov 01

Dynamics & probability: Asaf Katz (HUJI): Mixing and sparse ergodic theorems

2:00pm to 3:00pm

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
We consider Bourgain's sparse ergodic theorem for systems where quantitative mixing estimates are present. Focusing on the case of the horocyclic flow, we show how to use such
estimates in order to bound the dimension of the exceptional set, providing evidence towards conjectures by N. Shah, G. Margulis and P. Sarnak. Moreover we show that there exists a bound which is independent from the spectral gap. The proof uses techniques from homogeneous dynamics, automorphic representations and number theory.
2017 Jun 27

Dynamics seminar:Ohad Feldheim (Stanford): The power of two-choices in reducing discrepancy

2:00pm to 3:00pm

Consider a process in which points are assigned uniformly and independently at random on the interval [0,1]. It is a classical observation that after N points were assigned, the typical discrepancy of the empirical distribution, i.e., the maximum difference between the proportion of points on any interval and the length of that interval, is of order 1/sqrt{N}. Now consider a similar online process in which at every step an overseer is allowed to choose between two independent, uniformly chosen points on [0,1].
2017 Mar 07

Dynamics seminar: Erez Nesharim: Badly approximable vectors in fractals

2:00pm to 3:00pm

In ergodic dynamical systems almost every point is generic. Many times it is interesting to understand how large is the set of non-generic points. In this talk I will present a criterion for a set to have a nonempty intersection with every “regular fractal". We then apply this criterion to
show that the set of badly approximable vectors with weights intersects every regular fractal, and put it in the context of diagonalizable actions on homogeneous spaces. 
This talk is based on a joint work with Dzmitry Badziahin, Stephen Harrap and David Simmons.
2016 Nov 22

Dynamics & probability, Vincent Delacroix (Bordeaux): Computing Lyapunov exponents of the Teichmüller flow

2:00pm to 3:00pm

Location: 

Bet Belgia Library, Hebrew University of Jerusalem
The Teichmüller flow acts as a renormalization operator for interval
exchange transformations. For this reason its properties give some insight
about the dynamics of rational billiards. For example Lyapunov exponents of
the Teichmüller flow are tightly related to equidistribution speed in
rational billiards. Since the mid 90's M. Kontsevich and A. Zorich started
computations of these exponents.
After giving some motivating examples for the computation of these exponents
and a brief overview of 30 years of intensive research (including works of
2017 Dec 05

Dynamics Seminar: Micheal Hochman (HUJI): Dimension of self-affine sets and measures

2:15pm to 3:15pm

Location: 

Ross 70
I will discuss joint work with Balazs Barany and Ariel Rapaport on the dimension of self-affine sets and measures. We confirm that under mild irreducibility conditions on the generating maps, the dimension is "as expected", i.e. equal to the affinity or Lyapunov dimension. This completes a program started by Falconer in the 1980s. In the first part of the talk I will explain how the Lyapunov dimension arises from Ledrappier-Young formula for self-affine sets, and then explain how additive combinatorics methods can be used to prove that this is the correct dimension.
2017 Nov 21

Dynamics Seminar: Yakov Pesin (PSU), “A geometric approach for constructing equilibrium measures in hyperbolic dynamics”

2:15pm to 3:15pm

Location: 

Ross 70
In the classical settings of Anosov diffeomorphisms or more general locally maximal hyperbolic sets I describe a new approach for constructing equilibrium measures corresponding to some continuous potentials and for studying some of their ergodic properties. This approach is pure geometrical in its nature and uses no symbolic representations of the system. As a result it can be used to effect thermodynamics formalism for systems for which no symbolic representation is available such as partially hyperbolic systems.

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