Journal Article: A spectral approach for quenched limit theorems for random hyperbolic dynamical systems
Dragičević, D., Froyland, G., González-Tokman, C. and Vaienti, S. (2020). A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373 (1) 629-664. doi:10.1090/tran/7943
Journal Article: Quenched stochastic stability for eventually expanding-on-average random interval map cocycles
Froyland, Gary, González-Tokman, Cecilia and Murray, R. U.A. (2019). Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39 (10) 2769-2792. doi:10.1017/etds.2017.143
Journal Article: Hilbert space Lyapunov exponent stability
Froyland, Gary, Gonzalez-Tokman, Cecilia and Quas, Anthony (2019). Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372 (4) 2357-2388. doi:10.1090/tran/7521
(2018–2020) University of New South Wales
Coherent structures in chaotic dynamical systems
(2016–2018) ARC Discovery Early Career Researcher Award
Ergodic theory and coherent structures for non-autonomous dynamical systems
Doctor Philosophy
Algorithms for the detection, tracking and investigation of coherent structures and their mixing properties in a non-autonomous dynamical setting
Doctor Philosophy
Synchronisation of Nanomechanical Oscillators
(2017) Doctor Philosophy
Dynamical Systems and Ergodic Theory
Topics available for student projects at PhD/Masters/Honours level include:
(i) Non-autonomous or random dynamical systems. These systems model the evolution of phenomena affected by external influences, such as deterministic forcing or stationary noise. Topics under investigation include Lyapunov exponents, multiplicative ergodic theory, statistical behaviour and stability.
(ii) Theoretical and computational analysis of metastable and coherent structures in dynamical systems. Such structures encode important information of the long term evolution and transport phenomena in the underlying system. For example, they are useful to identify, analyse and quantify features of natural phenomena such as oceanic eddies and atmospheric vortices.
González-Tokman, Cecilia (2018). Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems. Contributions of Mexican mathematicians abroad in pure and applied mathematics. (pp. 31-52) edited by .Guanajuato, Mexico: American Mathematical Society. doi:10.1090/conm/709/14290
A spectral approach for quenched limit theorems for random hyperbolic dynamical systems
Dragičević, D., Froyland, G., González-Tokman, C. and Vaienti, S. (2020). A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373 (1) 629-664. doi:10.1090/tran/7943
Quenched stochastic stability for eventually expanding-on-average random interval map cocycles
Froyland, Gary, González-Tokman, Cecilia and Murray, R. U.A. (2019). Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39 (10) 2769-2792. doi:10.1017/etds.2017.143
Hilbert space Lyapunov exponent stability
Froyland, Gary, Gonzalez-Tokman, Cecilia and Quas, Anthony (2019). Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372 (4) 2357-2388. doi:10.1090/tran/7521
A spectral approach for quenched limit theorems for random expanding dynamical systems
Dragičević, D., Froyland, G., González-Tokman, C. and Vaienti, S. (2018). A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360 (3) 1121-1187. doi:10.1007/s00220-017-3083-7
Almost sure invariance principle for random piecewise expanding maps
Dragicevic, D., Froyland, G., Gonzalez-Tokman, C. and Vaienti, S. (2018). Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31 (5) 2252-2280. doi:10.1088/1361-6544/aaaf4b
Optimal mixing enhancement by local perturbation
Froyland, Gary, Gonzalez-Tokman, Cecilia and Watson, Thomas M. (2016). Optimal mixing enhancement by local perturbation. SIAM Review, 58 (3) 494-513. doi:10.1137/15M1023221
Stability and approximation of invariant measures of Markov chains in random environments
Froyland, Gary and Gonzalez-Tokman, Cecilia (2016). Stability and approximation of invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16 (1) 1650003, 1650003.1-1650003.23. doi:10.1142/S0219493716500039
A concise proof of the multiplicative ergodic theorem on banach spaces
González-Tokman, Cecilia and Quas, Anthony (2015). A concise proof of the multiplicative ergodic theorem on banach spaces. Journal of Modern Dynamics, 9 (01) 237-255. doi:10.3934/jmd.2015.9.237
Froyland, Gary, Gonzalez-Tokman, Cecilia and Quas, Anthony (2015). Stochastic stability of Lyapunov exponents and Oseledets splittings for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68 (11) 2052-2081. doi:10.1002/cpa.21569
Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools
Froyland, Gary, Gonzalez-Tokman, Cecilia and Quas, Anthony (2014). Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1 (2) 249-278. doi:10.3934/jcd.2014.1.249
A semi-invertible operator Oseledets theorem
Gonzalez-Tokman, Cecilia and Quas, Anthony (2014). A semi-invertible operator Oseledets theorem. Ergodic Theory and Dynamical Systems, 34 (4) 1230-1272. doi:10.1017/etds.2012.189
Stability and approximation of random invariant densities for Lasota-Yorke map cocycles
Froyland, Gary, Gonzalez-Tokman, Cecilia and Quas, Anthony (2014). Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27 (4) 647-660. doi:10.1088/0951-7715/27/4/647
Ulam's method for Lasota-Yorke maps with holes
Bose, Christopher, Froyland, Gary, Gonzalez-Tokman, Cecilia and Murray, Rua (2014). Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13 (2) 1010-1032. doi:10.1137/130917533
Ensemble data assimilation for hyperbolic systems
Gonzalez-Tokman, Cecilia and Hunt, Brian R. (2013). Ensemble data assimilation for hyperbolic systems. Physica D: Nonlinear Phenomena, 243 (1) 128-142. doi:10.1016/j.physd.2012.10.005
Approximating invariant densities for metastable systems
Gonzalez Tokman, Cecilia, Hunt, Brian R. and Wright, Paul (2011). Approximating invariant densities for metastable systems. Ergodic Theory and Dynamical Systems, 31 (5) 1345-1361. doi:10.1017/S0143385710000337
Scaling laws for bubbling bifurcations
Gonzalez-Tokman, Cecilia and Hunt, Brian R. (2009). Scaling laws for bubbling bifurcations. Nonlinearity, 22 (11) 2607-2631. doi:10.1088/0951-7715/22/11/002
(2018–2020) University of New South Wales
Coherent structures in chaotic dynamical systems
(2016–2018) ARC Discovery Early Career Researcher Award
Ergodic theory and coherent structures for non-autonomous dynamical systems
Doctor Philosophy — Principal Advisor
Other advisors:
Algorithms for the detection, tracking and investigation of coherent structures and their mixing properties in a non-autonomous dynamical setting
Doctor Philosophy — Principal Advisor
Synchronisation of Nanomechanical Oscillators
(2017) Doctor Philosophy — Principal Advisor
Other advisors:
Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.
Dynamical Systems and Ergodic Theory
Topics available for student projects at PhD/Masters/Honours level include:
(i) Non-autonomous or random dynamical systems. These systems model the evolution of phenomena affected by external influences, such as deterministic forcing or stationary noise. Topics under investigation include Lyapunov exponents, multiplicative ergodic theory, statistical behaviour and stability.
(ii) Theoretical and computational analysis of metastable and coherent structures in dynamical systems. Such structures encode important information of the long term evolution and transport phenomena in the underlying system. For example, they are useful to identify, analyse and quantify features of natural phenomena such as oceanic eddies and atmospheric vortices.