Upcoming talks:
| 10 X | Françoise Pene (Université de Bretagne Occidentale) Central Limit Theorem for billiards in some unbounded domains Show abstract I will present Central Limit Theorems for Birkhoff sums of
the billiard map and flow in some unbounded domains.
We will consider the case of the periodic Lorentz gas (with finite or
infinite horizon) and the case of billiards in dispersing domains with
unbounded cusps.
The results on the finite horizon periodic Lorentz gas have been
proved in collaboration with Damien Thomine. The results on billiards
with unbounded cusps are proved in an almost finished work in progress
with Marco Lenci and Hong-Kun Zhang.
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Show rest
| 20 VI | Marisa Cantarino (Monash University) A computer-assisted proof of robust transitivity
Show abstract
Given a diffeomorphism on the 3-torus, we present a
computer-assisted strategy to prove partial hyperbolicity, existence
of a blender in a given region and robust transitivity --- properties
which we introduce briefly with examples. These proofs are implemented
for a family of systems. This work in preparation is a collaboration
with Andy Hammerlindl and Warwick Tucker.
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| 20 VI | Natalia McAlister (Monash University) A computer-assisted proof of the existence of blenders for a
3-dimensional Hénon-like family Show abstract In this project we develop a computer program to verify the
existence of blenders for concrete examples. A blender is a hyperbolic
set whose unstable manifold, when looking at certain intersections,
seems to have a greater dimension than it actually does. This
descriptive definition cannot be verified on a computer. The first
step is then stating necessary conditions for establishing the
existence of a blender in a computer-friendly way. Then, we develop an
algorithm to verify said conditions. Using this algorithm, we prove
the existence of blenders for a family of maps defined as a skew
product over the Hénon map. This algorithm could be extended to other
quadratic maps, and potentially to other more challenging examples.
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The seminar takes place on Fridays
at 10.15-11.45 AM (Kraków time) - currently CET (UTC+1) in the room 1016
of the Jagiellonian University
Department of Mathematics
and Computer Science
(ul. Łojasiewicza 6, Cracow).
