Sydney Dynamics Group




SDG workshop: Multiscale dynamical systems - theory and application, Blackheath, Blue Mountains, 2-5 November 2015



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.
  • Sasha Fish (USyd, Maths): Ergodic theory, applications of dynamics to number theory.
  • 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.
  • Milena Radnovic (USyd, Maths): integrable systems, billiards.
  • John Roberts (UNSW, Maths): discrete integrable systems, symmetry and time-reversal symmetry, algebraic dynamics.
  • Geoff Vasil (USyd, Maths): geophysical and astrophysical fluid dynamics, multi-scale methods, pattern formation.
  • 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): Pattern formation, biomathematics, anomalous diffusion.
  • Davor Dragicevic (UNSW, Maths): hyperbolic dynamical systems and ergodic theory
  • Jeroen Wouters (USyd, Maths): dynamical systems, statistical mechanics, climate science
  • Atiya Zaidi (UNSW, Maths): discrete integrable systems

    Graduate students:

  • Kamil Bulinski (USyd, Maths): Applications of dynamics and ergodic theory to number theory
  • Tony Chung (UNSW, Phys): Gram-Schmidt Lyapunov vectors at equilibrium
  • Isaac Donnelly (UNSW, Maths): Complex networks
  • Brent Giggins (USyd, Maths): Forecasting with covariant Lyapunov vectors
  • Ngan Kim Le (UNSW, Maths): Numerical methods for stochastic PDEs
  • Eric Kwok (UNSW, Math): Ergodic theory and geometry of dynamical systems
  • John Mitry (USyd, Maths): Dynamical systems theory methods in mathematical biology
  • Ignacio Ortega Piwonka (UNSW, Maths): Fractional diffusion
  • Kerry Roberts (USyd, Maths): Geometric singular perturbation theory and averaging
  • 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
  • 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
  • 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
  • John Wormell (USyd, Math): Linear response theory in chaotic deterministic 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 2016:

  • 22/01/16: Henk Bruin (Vienna) "Sharp mixing rates via inducing w.r.t. general return times"
  • 19/02/16: Sandro Vaienti (Marseille) "Statistical properties of non-autonomous (sequential) dynamical systems: limit theorems and extreme values"
  • 04/04/16: Michael Bjorklund (Chalmers) "Quasi-crystals, Fourier analysis and ergodic theory. Lecture 1"
  • 08/04/16: Michael Bjorklund (Chalmers) "Quasi-crystals, Fourier analysis and ergodic theory. Lecture 2"
  • 11/04/16: Michael Bjorklund (Chalmers) "Quasi-crystals, Fourier analysis and ergodic theory. Lecture 3"
  • 15/04/16: Michael Bjorklund (Chalmers) "Quasi-crystals, Fourier analysis and ergodic theory. Lecture 4"
  • 18/04/16: Michael Bjorklund (Chalmers) "Quasi-crystals, Fourier analysis and ergodic theory. Lecture 5"
  • 22/04/16: Andy Hammerlindl (Monash) "Surgery on Anosov flows and new partially hyperbolic examples"
  • 17/06/16: Nick Pizzo (University of California San Diego) "Properties of nonlinear and breaking deep-water surface waves"
  • 29/06/16: Yury Stepanyants (Southern Queensland) "Modulational instability of quasi-harmonic wave-trains in rotating fluids"
  • 26/07/16: Philippe Guyenne (Delaware) "The surface signature of internal waves in the ocean"

Maintained by Georg Gottwald