Abstracts INVITED TALKS Adam EPSTEIN (Warwick University)A Newhouse Phenomenon in Transcendental Dynamics In joint work with Lasse Rempe-Gillen, we prove the existence of bounded type entire maps with infinitely many attractors. We obtain such bounded type maps by surgery on finite type maps with appropriate dynamics. We obtain additional control when the latter are selected from the $cos \sqrt{z}$ family. Download the slides. Dan NICKS (University of Nottingham)Fast escape using normal families Eremenko proved that for a transcendental entire function the escaping set is non-empty. In particular, he used Wiman-Valiron theory to construct points with forward orbits that tend to infinity fast, compared to an iterated maximum modulus. Research in "quasiregular dynamics" aims to generalise results from complex dynamics by studying the iteration of quasiregular mappings of R^n. Such quasiregular maps are a natural generalisation of entire functions, although no version of Wiman-Valiron theory is available. However, many results about normal families (including Montel's theorem) do generalise to this new setting and these have been used to construct fast escaping points for quasiregular maps. This approach gives an alternative method of proof in the original complex setting and, in fact, this leads us on to a result about the asymptotic rate of escape that appears to be new even for entire functions. Download the slides. Mary REES (University of Liverpool)Persistent Markov Partitions in Complex Dynamics Markov partitions are ubiquitous in dynamics, usually simply for providing recognisable dynamical systems up to conjugacy. But Markov partitions are especially useful in complex dynamics, because they can be used, not only to describe the dynamics of individual dynamical systems, but also to describe variation of dynamics on open subsets of parameter space. In fact what is used is not a single Markov partition but a sequence of them, which has come to be known as a puzzle, following Yoccoz, who first used what is known as the Yoccoz puzzle for quadratic polynomials. The corresponding sequence of puzzles of parameter space is known as the (Yoccoz) parapuzzle. I shall say something about the history of the use of such puzzles, and about a fairlly general construction of such puzzles which I have been studying. Download the slides. Gwyneth STALLARD (The Open University)The structure of the escaping set of a transcendental entire function The escaping set of a transcendental entire function consists of the set of points that escape to infinity under iteration and, in recent years, has come to play a key role in complex dynamics. Much work has been motivated by Eremenko's conjecture that all the components of the escaping set are unbounded. Significant progress has been made by studying the set of points that escape as fast as possible and it is known that all the components of the fast escaping set A_R(f) are unbounded. We show that, either A_R(f) has uncountably many components (as for the exponential function) or it is connected and has the form of a spiders web.This is joint work with Phil Rippon. Download the slides. Sebastian VAN STRIEN (Imperial College London)Quasi-symmetric rigidity in one-dimensional dynamics and applications In this talk I will discuss quasisymmetric rigidity in real dimension one. Building on earlier work with Weixiao Shen and Oleg Kozlovski, recently Trevor Clark and I have shown that under some additional very weak conditions two topologically conjugate C^3 interval maps are quasi symmetrically conjugate. CONTRIBUTED TALKS Simon ALBRECHT (Christian-Albrechts-Universität zu Kiel)On the construction of entire functions in the Speiser class It was proven by Gwyneth Stallard that for any 1

 Contact us at:Vasso EvdoridouVasiliki.Evdoridou@open.ac.ukDavid Martí PeteDavid.MartiPete@open.ac.uk We are proudly sponsored by: Last updated: November 2014Department of Mathematics and StatisticsThe Open UniversityWalton Hall, Milton Keynes MK7 6AAUnited Kingdom