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 (USyd, 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.
  • Ray Kawai (USyd, Maths): statistics and numerical methods for stochastic differential equations, mathematical ecology, mathematical finance, optimization
  • Shane Keating (UNSW, Maths): Mixing and stirring in geophysical turbulence; satellite altimetry; ocean state estimation; eddy parameterization.
  • 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.
  • Robert Marangell (USyd, Maths): dynamical systems, stability of nonlinear waves.
  • 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:

  • Chris Angstmann (UNSW, Maths)
  • James Atkinson (USyd, Maths): integrable systems, discrete equations.
  • Cecilia González Tokman (UNSW, Maths): dynamical systems and ergodic theory.
  • Andy Hammerlindl (USyd/UNSW, Maths): dynamical systems and ergodic theory.
  • Misha Neklyudov (USyd, Maths): stochastic PDEs.
  • 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): Numerical multiscale methods
  • 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
  • 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
  • Thomas Watson (UNSW, Maths): Computing covariant Lyapunov vectors; geometric and probabilistic flux in dynamical systems
  • Joachim Worthington (USyd, Math): Stability theory in Hamiltonian and volume-preserving dynamical systems

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 2013:

  • 22/01/13: Vladimir Gaitsgory (Flinders University) "Linear Programming and averaging approaches to singularly perturbed optimal control problems"
  • 01/02/13: David Kelly (University of Warwick) "Homogenisation for multidimensional maps"
  • 08/03/13: Cecilia Gonzalez Tokman "Stability and approximation of random invariant densities via a multiplicative ergodic theorem"
  • 22/03/13: Shane Keating "Stochastic data assimilation methods for ocean state estimation"
  • 03/04/13: Carola-Bibiane Schoenlieb (Cambridge) "Noise estimation by PDE-constrained optimisation"
  • 04/04/13: Ian Melbourne (University of Warwick) "Mixing and rates of mixing for continuous time infinite measure systems"
  • 19/04/13: Sasha Fish "Product sets in amenable groups through a dynamical approach"
  • 03/05/13: Federico Frascoli (University of Melbourne) "Anti-tumor immunity and growing cancers: a dynamical system approach"
  • 24/05/13: Ray Kawai "Mathematical programming gives hard bounds of the Dirichlet problem ßfor partial differential equations"
  • 31/05/13: Christian Franzke (British Antarctic Survey, Cambridge) TBA
  • 07/06/13: Holger Dullin "Two new integrable systems related to the Euler equations on a rotating sphere"

Maintained by Georg Gottwald