please post: ---------------------------------------------------------------------------------------------- London Dynamical Systems Group ---------------------------------------------------------------------------------------------- LDSG annual London Dynamical Systems Workshop 2010 http://www.ma.ic.ac.uk/DynamIC/LDSG2010 Thursday 29 April 2010 Department of Mathematics, Imperial College London Huxley Building, 180 Queens Gate, London SW7 2AZ (All talks will be in room 140, level 1 [basement]) Program: 09:30-10:15 Rod Halburd (University College) Arithmetic, analysis and integrability 10:15-11:00 Dmitry Turaev (Imperial College) Abundance of weak attractors with all zero Lyapunov exponents 11:00-11:30 coffee break 11:30-12:15 Sergey Zelik (Surrey) Soliton interaction and space-time chaos in a driven Ginzburg-Landau equation 12:15-13:00 Franco Vivaldi (Queen Mary) Order vs. chaos when the space is discrete 13:00-14:00 lunch break 14:00-14:30 Oleg Makarenkov (Imperial College) Bifurcation of asymptotically stable periodic solutions in impact systems 14:30-15:00 David Sinden (University College) Integrability, localisation and bifurcation of an elastic conducting rod in a magnetic field 15:00-16:00 tea-break with phd posters Neil Bristow (Surrey): Alternating period-doubling cascades Jeremy Chamard (Surrey): Locating saddle-type solutions of quasi-linear problems using the string method Jonith Fischmann (QMUL): Eigenvalues of real and complex random matrices Timothy Grant (Surrey): Preservation of conservation laws with finite differences for KdV Christopher Knight (Surrey): Changes in stability of stationary fronts in wave equations with an inhomogeneous nonlinearity Georgie Knight (QMUL): Chaotic diffusion in dynamical systems Kristian Kristiansen (Surrey): Almost invariance of a slow manifold with bifurcation in a two degree of freedom Hamiltonian system Friedrich Lenz (QMUL): Velocity distributions of foraging bumblebees Chris Warner (Imperial): Unbounded energy growth in Hamiltonian systems under small perturbations with chaotic potentials 16:00-16:30 Dalia Terhesiu (Surrey) Asymptotics of the transfer operator in the infinite case 16:30-17:00 Eric van der Straeten (Queen Mary) Superstatistics: past, present and future PhD students are invited to present their research projects and/or results in the form of a poster, that the attendants can consult during the one-hour afternoon tea-break. We would like to ask all students that intend to present a poster, to inform Martin Rasmussen (m.rasmussen@imperial.ac.uk). For updates of the program, inclusive posters, please see http://www.ma.ic.ac.uk/DynamIC/LDSG2010 Local organizers: Jeroen Lamb (j.lamb@imperial.ac.uk) Martin Rasmussen (m.rasmussen@imperial.ac.uk) Abstracts: SPEAKER: Franco Vivaldi TITLE: Order vs. chaos when the space is discrete ABSTRACT: In dynamical systems with discrete space, the distinction between regular and irregular motions must be re-considered. I articulate the main questions, and summarize some recent research. SPEAKER: Erik Van der Straeten TITLE: Superstatistics: past, present and future ABSTRACT: The crucial assumption of superstatistics is the existence of a parameter $\beta$ that fluctuates on a large time scale as compared to the other time scales of a system under consideration. This parameter $\beta$ is usually interpreted as an inverse temperature. This means that the system under consideration is a non-equilibrium system from a thermodynamic point of view. As the title suggests, this talk consists of three parts. In the first part, I will outline the general ideas of superstatistics. In the second part, I will briefly discuss the superstatistical analysis of real time series. In the third part, I will share with the audience what I think is the next challenge in superstatistical model building. SPEAKER: David Sinden TITLE: Integrability, localisation and bifurcation of an elastic conducting rod in a magnetic field ABSTRACT: Motivated by the problem of electrodynamic space tethers we consider the equilibrium equations for a elastic conducting rod in a magnetic field. In body coordinates the equations are found to sit in a family of noncanonical Hamiltonian systems. These systems, which include the classical Euler and Kirchhoff rods, are shown to be completely integrable under certain material conditions. Melnikov's method is then used to show that under two integrable perturbations can in fact destroy the integrable structure, resulting in multimodal rod configurations. Such solutions are investigated numerically revealing a rich bifurcation structure: a codimension-two point defining a double Hamiltonian-Hopf bifurcation acts as an organising centre. ---------------------------------------------------------------------------------------------- LDSG is a collaboration between the dynamical systems groups at Imperial College London, Queen Mary University of London, University College London and the University of Surrey. Its meetings are financially supported by the London Mathematical Society (LMS). ----------------------------------------------------------------------------------------------