Alexey Okunev - Dynamical Systems and Analysis Seminar Series
|Starts:||15:00 24 May 2021|
|Ends:||16:00 24 May 2021|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, External researchers, Adults, Alumni, Current University students|
Alexey Okunev will be speaking at this research seminar, part of the Dynamical Systems and Analysis seminar series.
Title: Step skew products with circle or interval fibre
Abstract: An iterated function system is a tuple of smooth maps (in this talk orientation-preserving diffeomorphisms) from some manifold M to itself.
The dynamics of the semigroup generated by an IFS can be naturally encoded by one map, a skew product over Bernoulli shift with the fibre M.
The fibre maps of this skew product depend only on the zeroth element of the sequence in the base, such skew products are called step skew products.
As the dynamics in the base is "hyperbolic", step skew products can be considered toy examples of partially hyperbolic dynamical systems.
We will discuss the following phenomena exhibited by step skew products with one-dimensional fibre:
- bony attractors
- non-hyperbolic ergodic measures
- universal dynamics
- intermingled basins
- thick attractors.
Then we will talk about the following result: generic step skew product with circle fibre either is robustly transitive or has an absorbing domain (the base times a finite disjoint union of intervals). In the second case the skew product can be reduced to a skew product with interval fibre.
Organisation: University of Loughborough
Travel and Contact Information
Alan Turing Building