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ETDS 2011-12

Welcome to the Ergodic Theory and Dynamical systems seminars web page!
The seminars are held on Tuesdays at 14:00 in Room B3.02 - Mathematics Institute

Organizer: Davoud Cheraghi

Term 3

  • Tuesday 29 May 2012
    Alastair Fletcher (Warwick)
    Decomposing diffeomorphisms of the sphere
     
  • Tuesday 12 June 2012
    Katsutoshi Shinohara (Uni)
    On the (non)-minimality of free-semigroup actions on the interval C^1-close to the identity

    Abstract:
    We consider (attracting) free semigroup actions (with two generators) on an interval.
    It is known that, if those two maps are sufficiently C^2-close to the identity, then
    there is a restriction on the shape of the (forward) minimal set. Namely, it must be
    an interval. (This statement is not accurate. I will give the precise statement in my
    talk.) In this talk, I will explain that the similar argument fails in C^1-topology.
     

  • Thursday 14 June 2012
    Arnaud Cheritat (Institut de Mathematique de Toulouse)
    The talk is moved to Friday!

  • Wednesday 20 June 2012 - room MS.05
    Olga Lukina (University of Leicester)
    Hierarchy of graph matchbox manifolds
    Abstract:
    We study a class of graph foliated spaces, or graph matchbox manifolds, initially
    constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier
    of dynamical complexity which we call a level. We develop the fusion construction,
    which allows us to associate to every two graph foliated spaces a third one which
    contains the former two in its closure. Although the underlying idea of the fusion
    is very simple, it gives us a powerful tool to study graph foliated spaces.
    Using fusion, we prove that there is a hierarchy of graph foliated spaces at infinite
    levels. We also construct examples of graph foliated spaces at low levels.

Term 2

  • Tuesday 17 January 2012
    Mark Pollicott (Warwick)
    The Schottky-Klein Function and Ergodic Theory
  • Tuesday 24 January 2012
    Adam Epstein (Warwick)
    Quadratic Mating Discontinuity

    Abstract: Mating is a partially defined operation which sends pairs of normalized
    polynomials of the same degree to normalized rational maps of that degree.
    As proposed by Douady, the recipe is to glue filled-in Julia sets back-to-back along
    opposite prime ends, in the hope of obtaining a branched self-cover of a topological
    sphere which is suitably conjugate to a unique normalized endomorphism of the
    Riemann sphere. We will show that this procedure yields a highly discontinuous
    map between the relevant parameter spaces.
  • Tuesday 31 January 2012
    Davoud Cheraghi (Warwick)
    Optimal estimates on perturbed Fatou coordinates
  • Tuesday 7 February 2012
    Dimitry Turaev (Imperial College London)
    On stickiness and flicker-noise
  • Tuesday 14 February 2012
    Peter Hazard (Warwick)
    Entropy without Periodic Points in Dimension Two

    Abstract: In 1980 A. Katok showed that if a $C^{1+\alpha}$-diffeomorphism $f$ of
    a compact surface has positive topological entropy then it has a homoclinic point.
    Consequently $f$ possesses a horseshoe, and hence infinitely many periodic orbits.
    It was asked if this held for $f$ with lower regularity. M. Rees later gave a counter-
    example, constructing a homeomorphism of the 2-torus with positive entropy which
    is minimal.
  • Tuesday 21 February 2012
    James Langley (University of Nottingham)
    Non-real zeros of derivatives of real meromorphic functions

    Abstract: Around 1911 Wiman conjectured that if an entire function is real on the
    real axis and, together with its second derivative, has only real zeros, then the
    function belongs to the Laguerre-Polya class, from which it follows that all derivatives
    have only real zeros. This has now been proved via a combination of results by
    several authors including the speaker, as have some related conjectures advanced
    by Polya in the 1940s. The talk will survey results in this direction and report on
    recent progress towards an analogue of the Polya-Wiman conjectures for functions
    which are meromorphic rather than entire.
  • Tuesday 28 February 2012
    Ian Morris (University of Surrey)
    Structure of extremal matrix products

    Abstract: The joint spectral radius of a finite or compact set of dxd matrices is the
    maximum possible exponential growth rate of long products of matrices drawn from
    that set. An influential conjecture of J. Lagarias and Y. Wang stated that for any
    finite set of matrices, this optimal rate of growth is achieved by a periodic product.
    We discuss counterexamples and describe the properties which must be satisfied
    by sequences of extremal growth.
  • Tuesday 6 March 2012
    Boguslaw Zegarlinski (Imperial College London)
    TBA
  • Tuesday 13 March 2012
    John Osborne (Open University)
    Spiders' webs and locally connected Julia sets of transcendental entire functions

    Abstract: In this talk, I will explore some links between the local connectedness of
    the Julia set of a transcendental entire function, and a particular geometric form
    of the Julia set known as a spider's web (first defined by Rippon and Stallard).

Term 1
  • Tuesday 11 October 2011
    Rodney Halburd (University College London)
    Title: Analysis, arithmetic and integrability

     
    Abstract: The behaviour of solutions of differential equations in the complex domain
    has long been used as a detector of integrability. In this talk, complex analytic and
    number theoretic properties of solutions of difference equations will be discussed
    that correlate well with integrability. Classification results will be presented showing
    how these properties naturally single-out the discrete Painlev\'e equations from
    more general classes of equations.
  • Tuesday 18 October 2011
    Jörn Peter (Kiel, Germany)
    Title:Hausdorff measure of Julia sets for bounded type functions of finite order
  • Tuesday 25 October 2011
    No meeting this week!
  • Tuesday 1 November 2011
    Alex Clark (University of Leicester)
    Title: Dynamics of matchbox manifolds

    Abstract: Matchbox manifolds are a particular type of lamination or foliated space
    in which the transverse space is totally disconnected. In this talk we will review the
    basic definitions and constructions and examine recent results with Steve Hurder
    establishing connections between the dynamics of matchbox manifolds and their
    topology. We will also discuss ongoing research with Hurder and Lukina that leads
    to a general framework for studying matchbox manifolds.


  • Tuesday 8 November 2011
    Franco Vivaldi (Queen Mary, London)
    Regular motion and anomalous tranport in a piecewise isometric system
  • Tuesday 15 November 2011,
    Yusuke Okuyama (Kyoto Institute of Technology)
    Singularities of Schro\"oder maps and unhyperbolicity of rational functions

    Abstract: One of the aims of this talk is to give a formulation of Fatou's hyperbolic
    density problem for unicritical families in terms of Schro\"oder (Poincar\'e) maps
    with respect to repelling periodic points of these unicritical polynomials. We really
    study the relationship between transcendental singularities or asymptotic values
    of Schro\"oder maps and un(semi)hyperbolicity of rational functions using both
    dynamics of rational functions and covering theoretical results on meromorphic
    functions.

    This talk is based on our joint work with David Drasin (Purdue).

  • Tuesday 22 November 2011, 2-3pm in Room B3.02
    Alfonso Sorrentino (Cambridge)
    Minimal average action and Hamiltonian dynamics

    Abstract: In the variational study of Tonelli Hamiltonian systems an important role
    is played by the so-called Mather’s minimal average action (also known as
    "beta-function" or "effective Lagrangian"), with particular attention to its regularity
    and symplectic properties. In this talk I'll discuss how, in the case of Hamiltonians
    on closed surfaces, its differentiabilty relates to the existence of invariant
    Lagrangian graphs and to the integrability of the system. Time permitting, I'll also
    describe a geometrical interpretation of this function in terms of the asymptotic
    distance from the identity in the group of Hamiltonian diffeomorphisms.
  • Tuesday 22 November 2011, 4-5pm in Room B3.03
    Vered Rom-Kedar (Weizmann Institute)
    A saddle in a corner - a model of atom-diatom chemical reactions

    Abstract: A geometrical model which captures the main ingredients governing
    atom-diatom collinear chemical reactions is proposed. This model is neither
    near-integrable nor hyperbolic, yet it is amenable to analysis using a combination
    of the recently developed tools for studying systems with steep potentials and
    the study of the phase space structure near a center-saddle equilibrium. The
    nontrivial dependence of the reaction rates on parameters, initial conditions
    and energy is thus qualitatively explained. Conditions under which the phase
    space transition state theory assumptions are satisfied and conditions under
    which these fail are derived. Extensions of these ideas to other impact-like
    systems and to other models of reactions will be discussed.

    Joint works w L. Lerman and M. Kloc.
  • Tuesday 29 November 2011
    Jon Aaronson (Tel-Aviv University)
    On the categories of weak mixing in infinite measure spaces

    Abstract: I will discuss some propositions such as "in general" an infinite measure
    preserving trasformation is subsequence rationally weakly mixing, but not rationally
    weakly mixing.
  • Tuesday 6 December 2011
    Martin Rasmussen (Imperial college London)
    Morse decomposition of nonautonomous dynamical systems