Events

Date: 20 May 2026

Location: MB-503

1pm: Mélodie Andrieu (Université Littoral): A Normality conjecture on rational base number systems

2pm: José Alves (Universidade do Porto): Linear response for skew-product maps

3.30pm: Selim Ghazouani (University College London): Speculations about parabolic dynamical systems

4.30pm: Zhiyuan Zhang (Imperial College London): Ergodicity of conservative random dynamics

Abstracts:

Mélodie Andrieu: A Normality conjecture on rational base number systems

The rational base number system, introduced by Akiyama, Frougny, and Sakarovitch in 2008, is a generalization of the classical integer base number system. Within this framework two interesting families of infinite words emerge, called minimal and maximal words. We formulate the conjecture that every minimal and maximal word is normal over an appropriate subalphabet.
The aim of the talk is to convince the audience that the conjecture seems true and of considerable difficulty. In particular, we shall discuss its connections with several older conjectures, including the existence of Z-numbers (Mahler, 1968) and Z-p/q-numbers (Flatto, 1992), the existence of triple expansions in rational base p/q (Akiyama, 2008), and the Collatz-inspired '4/3 problem' (Dubickas and Mossinghoff, 2009).
The talk is based on a joint work with Shalom Eliahou and Léo Vivion.

José Alves: Linear response for skew-product maps

We study linear response for families of skew-product dynamical
systems with mean contracting fibres. Using a sectional transfer
operator acting on families of probability measures along the fibres,
we describe invariant measures of the skew-product through sample
measures over the base dynamics, independently of the invertibility of
the base map. Under general assumptions we prove existence, uniqueness
and differentiability of invariant sample measures with respect to
system parameters. As applications, we obtain linear response for some
variations of baker maps and for physical measures of solenoidal
attractors with intermittency, a class of partially hyperbolic systems
beyond the reach of standard transfer operator methods.

Selim Ghazouani: Speculations about parabolic dynamical systems

A parabolic dynamical system is a dynamical system which displays polynomial sensitivity to initial conditions. These are pretty rare in physics but often pop up in homogeneous dynamics and number theory. In this talk we will try and make a case for the following meta-conjecture : the generic parabolic system satisfies the central limit theorem. This case will be based on extensive numerical experiments and a heuristic of probabilistic nature.

Zhiyuan Zhang : Ergodicity of conservative random dynamics

We prove ergodicity of conservative random dynamics satisfying a certain hyperbolicity condition. The new feature of our result is that we do not require the non-existence of zero Lyapunov exponents. As a particular application, we show that if R_1, R_2 in SO(d + 1), d ≥ 2, generate a dense subgroup, then any pair (f_1, f_2) of infinitely smooth volume preserving diffeomorphisms of the d-dimensional sphere that is sufficiently close to (R_1, R_2) is ergodic with respect to the volume. Previously this was only known to hold when d is even by a result of Dolgopyat and Krikorian. Joint work in progress with Jonathan DeWitt and Dmitry Dolgopyat.

One Day Ergodic Theory Meeting is a "wandering" seminar series supported by an LMS grant and organised by 15 UK universities: Birmingham University, Bristol University, Brunel University, Durham University, Exeter University, Glasgow University, Imperial College London, Loughborough University, Manchester University, The Open University, Queen Mary University of London, Surrey University, St. Andrews University, University College London and Warwick University.

The May 2026 Ergodic Theory Meeting will be hosted by the School of Mathematical Sciences at Queen Mary University of London.