Upcoming talks:
| 28 XI | Maciej Capiński (AGH) Characterising blenders via covering relations and cone conditions Show abstract
A blender is a hyperbolic set whose stable (or unstable)
manifold behaves as if it had higher dimension than the actual stable
(unstable) bundle of the hyperbolic set. We will present a simple
construction based on correct topological alignment of sets and cone
conditions that leads to the creation of blenders. If time permits, we
will also describe how this method leads to robust intersections of
the stable and unstable manifolds of two blenders, producing the
so-called heterodimensional cycles.
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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).
