Sydney Dynamics Group



SDG new year's BBQ at Coogee Beach (January 12, 2009); front from left: Naratip Santitissadeekorn, Gary Froyland, Martin Wechselberger, Georg Gottwald, Edgar Knobloch (visitor); back from left: Ognjen Stancevic, Sebastian Reich (visitor), Simon Lloyd, John Roberts, Dave Galloway, Charlie Macaskill.



The SDG was founded in January 2007 as a cooperation of faculty members between two of the major universities in Sydney, Australia, the University of New South Wales (UNSW) and the University of Sydney (USyd). The group's research missions span topics in pure and applied dynamical systems, ranging from algebraic dynamics, ergodic theory, and Hamiltonian dynamics to rhythms in physiological systems, time series analysis, geophysical fluid dynamics and statistical mechanics.

    Members of the group:

  • Holger Dullin (USyd, Maths): Hamiltonian systems, rigid body dynamics with applications in biomechanics, topology of integrable systems, semiclassical quantization, volume preserving mappings.
  • Gary Froyland (UNSW, Maths): smooth and numerical ergodic theory, applications to atmospheric and oceanic flows.
  • Dave Galloway (USyd, Maths): solar and geodynamo modelling.
  • Ben Goldys (UNSW, Maths): stochastic partial differential equations, analysis on infinite-dimensional spaces, long time behaviour of solutions to stochastic ordinary and partial differential equations, optimal control.
  • Georg Gottwald (USyd, Maths): geophysical fluid dynamics, pattern formation in biological and chemical systems, nonlinear time series analysis.
  • Peter Kim (USyd, Maths): mathematical biology, cancer modelling, agent-based models
  • Charlie Macaskill (USyd, Maths): geophysical fluid dynamics, especially vortex dynamics and internal waves, acoustics in complex and random media with applications in biomedical ultrasound, mathematical theory of combustion.
  • Gary Morriss (UNSW, Physics): statistical mechanics of nonequilibrium systems.
  • Sheehan Olver (USyd, Maths): numerical analysis, integrable systems, random matrix theory.
  • John Roberts (UNSW, Maths): discrete integrable systems, symmetry and time-reversal symmetry, algebraic dynamics.
  • Martin Wechselberger (USyd, Maths): invariant manifold theory, canard theory, geometric singular perturbation theory with applications to the nervous system and cell signalling.

    Postdocs:

  • James Atkinson (USyd, Maths): integrable systems, discrete equations.
  • Robert Marangell (USyd, Maths): dynamical systems, stability of nonlinear waves
  • Natascha Neumärker (UNSW, Maths): algebraic dynamics.
  • Atiya Zaidi (UNSW, Maths): discrete integrable systems.

    Graduate students:

  • Tony Chung (UNSW, Phys): Gram-Schmidt Lyapunov vectors at equilibrium
  • Tim Glass (UNSW, Maths): Ergodic theory of affine stochastic differential equations
  • Ngan Kim Le (UNSW, Maths): Numerical methods for stochastic PDEs
  • John MacLean (USyd, Maths): Stochastic methods in geophysical fluid dynamics
  • John Mitry (USyd, Maths): Dynamical systems theory methods in mathematical biology
  • George Papadopoulos (USyd, Maths): Symplectic invariants of the Euler Top
  • Danya Rose (USyd, Maths): Geometric phase for periodic orbits in the 3-body problem
  • Ognjen Stancevic (UNSW, Maths): Metastability, escape rates, and topological entropy in deterministic and random dynamical systems; connecting open and closed dynamical systems
  • Robyn Stuart (UNSW, Maths): Connecting geometric and probabilistic descriptions of the dynamics of open systems
  • Duncan Sutherland (USyd, Maths): Geophysical flows and numerical methods for viscous fluid flows
  • William Tong (USyd, Maths): Geometric phase in multibody dynamics
  • Cuong Tran (UNSW, Maths): Stochastic equations with delays as limits of ARMA and GARCH processes
  • Daniel Truant (UNSW, Phys): Covariant Lyapunov vectors
  • Theo Vo (USyd, Maths): Geometric singular perturbation analysis of neuroendocrine models

An eigenfunction of a transfer operator highlights gyres in the Weddell and Ross Seas off the Antarctic Coast (Froyland et al., Phys. Rev. Lett. 98:224503, 2007)



Escape time diagram of the Levitron, a levitating magnetic top (Dullin, Regular and Chaotic Dynamics 9, 255-264, 2004)



Effect of coarse-graining on the Kac ring model (Gottwald & Oliver, SIAM Review 51, 613-635, 2009)

    Seminars 2012:

  • 13/01/12: Ian Melbourne (University of Surrey) "Operator renewal theory and mixing rates in infinite ergodic theory"
  • 27/01/12: Georg Gottwald "Diffusion and anomalous diffusion in spatially extended systems"
  • 09/03/12: Sheehan Olver "Sparse and stable spectral methods"
  • 16/03/12: Boris Kruglikov (University of Tromsø) "Hamiltonian integrability in geometry and relativity"
  • 30/03/12: Gary Froyland "Finite-time entropy: a probabilistic approach for measuring nonlinear stretching"
  • 10/04/12: Arieh Iserles (University of Cambridge) "Splittings, commutators and the linear Schrödinger equation"
  • 03/05/12: Jinqiao Duan (UCLA and Illinois Institute of Technology) "A glimpse of stochastic dynamics"
  • 18/05/12: Martin Wechselberger "Transonic evaporation waves in a spherical symmetric nozzle"

Maintained by Georg Gottwald