There will be dynamical systems meeting April 11-12 on the topic of Probabilistic methods for non-stationary dynamical systems. On Tuesday 13:30 – 17:15 we will have talks from Damien Thomine, Alexey Korepanov and Douglas Coates, held in Amory C501 (schedule, titles and abtracts bellow). On Wednesday 10:00-12:00 we will have an informal discussion on open problems in the area, short contributions of ~10-15mins to this session would be very welcome. If there is a problem or a topic which you would like to discuss during the Wednesday session, or you would like more information about the meeting please contact one of the organisers Mark Holland (m.p.holland@exeter.ac.uk), or Douglas Coates (dougcoates@fastmail.com).
Tuesday 11th April (13:30 – 17:15):
– 13:30-14:30 Damien Thomine (Universite Paris-Saclay). An application of the probabilistic potential theory to dynamical systems.
The probabilistic potential theory is the probabilistic counterpart of the classical potential theory, or in other words of the study of harmonic functions and their relations to probability theory. This theory offers the tools to compute transition probabilities for random walks, and for more general Markov chains. For instance, given any finite number of states, we can find the one the Markov chain is most likely to hit first.
In this talk, we shall present a dynamical variant of this question, that is, the computation of transition probabilities for extensions of measure-preserving dynamical systems. We shall show how one may recover these transitions probabilities in an asymptotic regime, using very diverse tools : transfer operators, metastable states, and perturbation of eigenvalues among others.
– 14:40-15:40 Alexey Korepanov (Loughborough). Loss of memory in nonstationary and mean-field-coupled intermittent dynamical systems.
I’ll talk about establishing optimal rates of decay of correlations and about moment bounds for sequential dynamics built with Liverani-Saussol-Vaienti maps (our pandemics-time project with Juho LeppƤnen), and about its recent application to mean-field-coupled systems (joint work with Wael Bahsoun).
– 15:40-16:15 Break
– 16:15-17:15 Douglas Coates (Exeter). “Persistent” non-statistical behaviour for interval maps with neutral fixed points
I will present recent work joint with Stefano Luzzatto in which we study a class F of full branched maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. We introduce a natural topology on the class F and show that there is a dense subset G of maps which are non-statistical (and in particular which have no physical measure). Moreover, we show that the non-statistical behaviour of the maps in G is “persistent” under a particular class of perturbations.
Wednesday 12th (10:00-12:00) informal discussion on open problems.