Upcoming talks:
| 24 X | Elias Rego (AGH) Robustly Transitive Sectional-Hyperbolic Classes Show abstract Sectional-hyperbolicity is a natural weakening of
hyperbolicity that plays a key role in understanding complex behaviors
arising in higher-dimensional flows, including Lorenz-like systems. In
this talk, I will discuss recent progress on the structure of
chain-recurrent classes in this setting. In particular, we will see
that, for a generic vector field, every nontrivial
sectional-hyperbolic chain-recurrent class is robustly a homoclinic
class. I will also explain how these results shed new light on the
dynamics of star flows. This is a joint work with Kendry Vivas.
|
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.
|
| 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.
|
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).
