### CSDC

The Centre for Systems, Dynamics and Control in the Department of Mathematics at the University of Exeter is a focus for interdisciplinary research on the modelling of complex systems, dynamical systems, control theory and their applications.

## Virtual Workshop: Early Warning Signs for Abrupt Transitions, 13th October 2021

This workshop is an online event under the EU Horizon 2020 funded project “TiPES – Tipping Points in the Earth System“. It is organized by Peter Ashwin, University of Exeter, Niklas Boers, Potsdam Institute for Climate Impact Research, and Kerstin Lux, Technical University of Munich.

https://www.ma.tum.de/de/fakultaet/news-events/early-warning-signs-abrupt-transitions.html

## Antipodeal Dynamics Workshop, 14th Oct 2021

There will be a collaborative Auckland-Exeter Virtual Workshop on Dynamical Systems on Thursday 14th October 2020, 8-10am (UK), 8-10pm (NZ).

• 8:00-8:20 Olga Podvigina (Moscow) “Chaos near heteroclinic networks”
• 8:20-8:40 Jan Sieber (Exeter) “Non-invasive control of randomly evolving networks”
• 8:40-9:00 Andrus Giraldo (Auckland) “Chaotic switching in driven-dissipative Bose-Hubbard dimers: Symmetry Increasing of chaotic attractors and degenerate singular cycles”
• 9:00-10:00 Virtual reality poster session

All welcome! Please register your interest using this form:

https://forms.gle/SSgqUmckZA7xZ17n6

We welcome posters: these will be hosted in a virtual reality poster room using Mozilla Hubs. You can contact one of the organizers if you have any questions.

Peter Ashwin (Exeter)

Claire Postlethwaite (Auckland)

## Vacancy: Postdoctoral research fellow on the dynamics of biomedical and healthcare models.

We are looking to recruit a Postdoctoral Research Fellow for a duration of 2.5 years to participate in one or more of a selection of projects investigating collective behaviours in dynamical systems models of processes of biomedical and healthcare relevance. These projects will be undertaken working with Prof Peter Ashwin and Dr Kyle Wedgwood as part of the EPSRC Hub for Quantitative Modelling in Healthcare at the University of Exeter. The specific project(s) will be tailored to the expertise and interests of the successful applicant. Example projects include studying pattern formation during embryonic development, generation of collective oscillations in neuronal networks, transitions in the progression of type 2 diabetes or reversibility of anti-microbial resistance. The successful applicant will liaise with collaborators (based at the University of Exeter and elsewhere) to develop and refine mathematical models of these systems and will apply numerical and analytical techniques to study the dynamics produced by these models.

The deadline for applications is 17th October 2021, with the post starting from 3rd Jan 2022.

https://www.jobs.ac.uk/job/CIC029/postdoctoral-research-fellow

## Lecturer/Senior Lecturers in Pure Mathematics (Mathematical Analysis)

We are seeking to appoint 2 full time posts, either Lecturer or Senior Lecturer in Pure Mathematics. The post/grade will be dependent on skills and experience. The posts will contribute to extending the research profile of mathematics at Exeter, and the application deadline is 16th 30th August 2021.

Applications are particularly encouraged from those working in areas of Mathematical Analysis (broadly interpreted) related or complementary to existing research strengths in the groups “Dynamical Systems and Analysis” and/or “Number Theory, Algebra and Geometry”. Your duties will cover all aspects of research, teaching and administration (see this link to advert and job specification for more details).

## PhD positions available in Dynamical Systems for 2021 entry

The following projects are available as part of the EPSRC EXE-MATH DTP funded studentship available for September 2021 entry. For eligible students, the studentship will provide funding of fees and a stipend which is currently £15,609 per annum for 2021-22.

To apply, see the links from each title, or go to: http://emps.exeter.ac.uk/studentships/

## Workshop on Nonautonomous dynamical systems: from theory to applications – July 5th, 2021

We are planning a one day workshop on nonautonomous dynamical systems with particular focus on climate change applications. It will be held at University of Exeter (Streatham Campus) on the 5th of July, with further opportunities to participate in informal discussions on 6th and 7th July. This is planned to be available for in-person (Exeter) and virtual participants.

## Exeter Workshop on Deterministic Extremes and Recurrence 21-23rd June 2021

This is a three-day workshop on deterministic extremes and recurrence in dynamical systems. This meeting will take place over Zoom, and access links/codes will be provided on this site closer to the time of the meeting (see below).

Contact Mark Holland, Surabhi Desai, Peter Ashwin, and Tomas Persson if you are interested and come back to here for more information in due course. Details are as follows.

### Attractors/measures (Newman)

Monday 21st June
Theme: Shrinking targets & recurrence

 13:45 Meeting opens 13.50 Introduction 14:00-14.45 Tomas Persson (Lund): Dynamical Borel–Cantelli lemmata, shrinking targets and recurrence 15:00-15.50 Henna Koivusalo (Bristol): Path-dependent, shrinking, moving targets and beyond, on generic self-affine sets 16:15-17:00 Tomas Persson. (2nd lecture). 17:00-17:30 Informal discussion

Tuesday 22nd June
Theme: Extremes, recurrence and limit laws in dynamical systems

 13:00-13.45 Mark Holland (Exeter): On the distribution of extreme events for dynamical systems 14:00-14.45 Mark Holland. (2nd lecture). 15:00-15.50 Meagan Carney (University of Queensland): Extremes for Energy-like Observables on Hyperbolic Systems. 16:15-17.05 Mike Todd (St Andrews): Capturing clustering in extreme values 17:05-17:30 Informal discussion

Wednesday 23rd June
Theme: Extremes and applications

 13:30-14.15 Tobias Kuna (Reading): A qualitative aspect of extreme value theory for dynamical systems 14:30-15.15 Tobias Kuna. (2nd lecture). 15.45-16.35 Julian Newman (Exeter): Attractors and attracting measures 16:35-17:00 Informal discussion

The 2×45 min sessions are mini-courses accessible to PhD students/post-doc researchers. The 50 minute talks are on general current research in the relevant themes.

### Abstracts

Meagan Carney (University of Queensland)
Extremes for Energy-like Observables on Hyperbolic Systems.

We consider an ergodic, measure-preserving dynamical system $(T, X, \mu)$ equipped with an observable $\phi: X\rightarrow R$. Given the stochastic process $X_n(x) = \phi(T^n(x))$, we establish an extreme value law for the sequence of maxima $M_n = max_{k\le n} X_k$ where $\phi$ is an energy-like observable and $(T, X, \mu)$ is hyperbolic. Observables of this form have the property that the set of maximization is a curve rather than a single point. We will discuss results in the case of Anosov diffeomorphisms, Sinai dispersing billiards, and coupled expanding maps. We will highlight the dependence of the extremal index on the set of maximization and discuss some numerical results for these systems.

Mark Holland (Exeter)
On the distribution of extreme events for dynamical systems
This lecture will cover almost sure growth bounds for maxima (extremes), using links to the theory of dynamical Borel Cantelli Lemmas. We also review distributional convergence results of extremes for dynamical systems, contrasting to the classical theory of extremes for i.i.d random variables.

Henna Koivusalo (Bristol)
Path-dependent, shrinking, moving targets and beyond, on generic self-affine sets
The classical shrinking target problem concerns the following set-up: Given a dynamical system (T, X) and a sequence of targets (B_n) of X, we investigate the size of the set of points x of X for which T^n(x) hits the target B_n for infinitely many n. In this talk I will study shrinking target problems in the context of fractal geometry. I will first recall the symbolic and geometric dynamical systems associated with iterated function systems, fundamental constructions from fractal geometry. I will then briefly cover the Hausdorff dimension theory of generic self-affine sets; that is, sets invariant under affine iterated function systems with generic translations. Finally, I will show how to calculate the Hausdorff dimension of shrinking target-type sets on generic self-affine sets. The target sets that I will consider move and shrink at a speed that depends on the path of x. Time permitting, further problems of similar flavour and refinements of the dimension result might also be explored. This talk is based on a joint work with Lingmin Liao and Michal Rams.

A qualitative aspect of extreme value theory for dynamical systems

Julian Newman (Exeter)
Attractors and attracting measures
Under mild assumptions, the SRB measure supported on an Axiom A attractor has the following two properties: (i) the empirical measure starting at a typical point near the attractor converges weakly to the SRB measure; (ii) the pushforward of any Lebesgue-absolutely continuous probability measure supported near the attractor converges weakly to the SRB measure. The first property is known as the “physical measure” property, and has been extensively studied and generalised. We will refer to the second property as the “attracting measure” property. It describes “mixing” behaviour, but in a more experimentally accessible way than just saying that the invariant measure itself is mixing: it can be expressed as a decay of “operational correlations” which make reference to the Lebesgue measure, as opposed to decay of “classical” correlations defined purely with respect to the invariant measure. There are various situations in the sciences, such as in climate science, where attractors have zero Lebesgue measure, and the question of whether such attractors support an attracting measure seems to be of high physical relevance. And yet, there appears to be very little literature addressing this question. (For example, is it known whether the physical measure on the classical Lorenz attractor is attracting?) I will present a topological generalisation of the original result of Bowen and Ruelle that establishes the attracting measure property for Axiom A flows.