22nd October 2015, CEMPS – University of Exeter, Organiser: Ana Rodrigues
Morning session (in Harrison Building, room HAR 171)
- 11:30 – 12:30 Paulo Varandas (UFBA, Brasil)
- 12:30 – 13:30 Thomas Jordan (Bristol, UK)
Afternoon session (in Laver Building, room Laver 212)
- 15:30 – 16:30 Peter Ashwin (Exeter, UK)
- 16:30 – 17:30 Yewie Zhang (Exeter, UK)
Paulo Varandas – Topological methods for problems in ergodic theory
Many chaotic dynamical systems are ‘rich’ from the topological viewpoint. This richness can be expressed by the fact that pseudo-orbits are shadowed by true orbits for the dynamics (shadowing property) or that pieces of orbits are well approximated by a orbit (specification property). These properties are satisfied by uniformly hyperbolic dynamics and some weaker versions have been established for wide classes of non-uniformly hyperbolic dynamical systems. In this talk we shall recall some of these weaker notions of shadowing and specification and describe how these can be used as very usefull tools in some problems arising in ergodic theory.
Thomas Jordan – Minkowski’s question mark function
Minkowski’s question mark function is a homeomprphism from [0,1] to itself which maps quadratic irrationals into the rationals. We’ll show how to view this function as a conjugacy between dynamical systems and as an invariant measure for the Gauss map (x\to 1/x\mod 1). We’ll then outline how a combination of large deviations and methods from a paper of Kaufman can be used to show the Fourier-Stieltjes transform of this function decays polynomially and give a few consequences of this fact. (Joint work with Tuomas Sahlsten).
Peter Ashwin – Piecewise isometric dynamics; some puzzles and problems
I will introduce and discuss some aspects of the dynamics of piecewise isometries (PWIs). These are iterated maps that are geometrically very simple (just isometries) on a number of “atoms” – convex regions that form a partition of phase space. They can be seen generalizations of interval exchange transformations to higher dimensions. PWis may arise in a number of applications but are hard to understand using standard dynamical tools based around hyperbolicity. I will outline a few results and some unsolved problems related to the dynamics, geometry and measure of the various invariant subsets that arise for PWIs in two dimensions.
Yewie Zhang – A glimpse of thermodynamics formalism for interval maps
I will take a short survey on the basic setting of thermodynamics formalism for interval maps. In particular, I will introduce the standard transfer operator method in the uniformly hyperbolic maps setting, and explain how the spectral structure of this operator links with the existence/uniqueness of equilibrium state and its exponential decay of correlation. I will also explain how to extend this method for the non-uniformly hyperbolic interval maps.
Program updates & changes
Late changes to programme (pdf for download)
We have organised a series of informal lectures about topics Mathematical Biology for the summer term 2015. More details of time and places are on
Please email Harun Baldemir if you have any queries or suggestions about this course.
Two funded PhD positions are available as part of the ITN “Critical Transitions in Complex Systems” (a EU Horizon 2020 Innovative Training Network). The posts last for 36 months.
Application closing date is 28 April 2015.
Note the eligibility criteria for EU Innovative Training Network positions. Usually UK residents are excluded, check http://ec.europa.eu/research/participants/portal/doc/call/h2020/h2020-msca-itn-2015/1622613-itn_2015_-_guide_for_applicants_v1_en.pdf#page=13 for details.
Ummu Atiqah Mohd-Roslan has just passed the viva for her PhD entitled “Stability index for riddled basins of attraction with applications to skew product systems”. Well done Atiqah!
Gerhard Keller from Erlangen http://www.min.math.fau.de/staff/keller-gerhard/prof-dr-gerhard-keller/ visited for a few days at the end of September 2014 to give a seminar to the group. His visit was supported by an LMS visitor grant – thanks to the LMS!
10 members of the Systems Biomedicine Group ventured out into Dartmoor, to the Two Bridges Hotel, for their first research retreat. During the first morning members took turn to receive updates from each other’s research teams. Then after lunch, PDRAs broke out, with leading Communications and Training expert John Oley, to focus on interview sills training, whilst PIs brain stormed ideas for new research grants and publications. An enjoyable dinner gave members the opportunity to get to know each other informally, before regrouping on Day 2. PDRAs focussed on communicating within multidisciplinary teams, whilst PIs built up outlines of grants, building on the discussions of day 1. After lunch, a short walk into Dartmoor followed by discussions on organising events associated with a recently awarded GW4 Building Communities award to Marc Goodfellow brought proceedings to a close.
First group retreat at the Two Bridges Hotel (from L to R) George Petkov, Helmut Schmidt, Rita Gupta, Ben Wareham, Jamie Walker, Ozgur Akman, Piotr Slowinski, Krasi Tsaneva-Atanasova, John Terry
Stefanie Zegowitz will be working with Ana Rodrigues. Her University homepage is http://emps.exeter.ac.uk/mathematics/staff/shz201.
The international conference “European Dynamics Days 2015” will be held at the University of Exeter during September 7th-11th 2015. Local organisers are
The current homepage of the conference is http://emps.exeter.ac.uk/mathematics/research/csdc/dynamicsdays2015/
We are moving to a system where all members of the blog can add news or make announcments about e.g. PhDs completed, upcoming workshops and conference etc. Watch this space!