Cecilia is an associate professor in the School of Mathematics and Physics at the University of Queensland. She has held research fellowships from the Australian Research Council (ARC) and the Pacific Institute for the Mathematical Sciences (PIMS). She has been a member of the Mexican National System of Researchers (SNI, 2014-2020).
Cecilia's service roles include: MATRIX Scientific Committee (2019-2022), Australian Mathematical Society council (2018-2021), and Queensland representative at the ANZIAM Executive Committee (2019-2021).
Journal Article: Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles
Gonzalez-Tokman, Cecilia and Quas, Anthony (2021). Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles. Journal of the European Mathematical Society, 23 (10), 3419-3457. doi: 10.4171/jems/1096
Journal Article: 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
Journal Article: 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
Journal Article: Stochastic stability of Lyapunov exponents and Oseledets splittings for semi-invertible matrix cocycles
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
What predictions can I trust? Stability of chaotic random dynamical systems
(2022–2025) ARC Discovery Projects
(2018–2021) University of New South Wales
Coherent structures in chaotic dynamical systems
(2016–2020) ARC Discovery Early Career Researcher Award
Random Dynamical Systems, Transfer Operators and Stability
Doctor Philosophy
(2021) Doctor Philosophy
(2021) 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.
Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles
Gonzalez-Tokman, Cecilia and Quas, Anthony (2021). Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles. Journal of the European Mathematical Society, 23 (10), 3419-3457. doi: 10.4171/jems/1096
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
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
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
Mexican Mathematicians in the World: Trends and Recent Contributions
Galaz-García, Fernando, González-Tokman, Cecilia and Pardo Millán, Juan eds. (2021). Mexican Mathematicians in the World: Trends and Recent Contributions. Contemporary Mathematics, Providence, Rhode Island: American Mathematical Society. doi: 10.1090/conm/775
Equilibrium states for non-transitive random open and closed dynamical systems
Atnip, Jason, Froyland, Gary, Gonzalez-Tokman, Cecilia and Vaienti, Sandro (2022). Equilibrium states for non-transitive random open and closed dynamical systems. Ergodic Theory and Dynamical Systems. doi: 10.1017/etds.2022.68
Invariant measures for random expanding on average Saussol maps
Batayneh, Fawwaz and González-Tokman, Cecilia (2022). Invariant measures for random expanding on average Saussol maps. Stochastics and Dynamics, 22 (3) 2250015, 1-18. doi: 10.1142/S0219493722500150
Lyapunov exponents for transfer operator cocycles of metastable maps: a quarantine approach
González-Tokman, C. and Quas, A. (2022). Lyapunov exponents for transfer operator cocycles of metastable maps: a quarantine approach. Transactions of the Moscow Mathematical Society, 82 (1), 65-76. doi: 10.1090/mosc/313
On the number of invariant measures for random expanding maps in higher dimensions
Batayneh, Fawwaz and Gonzalez-Tokman, Cecilia (2021). On the number of invariant measures for random expanding maps in higher dimensions. Discrete and Continuous Dynamical Systems- Series A, 41 (12), 5887-5914. doi: 10.3934/dcds.2021100
Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles
Gonzalez-Tokman, Cecilia and Quas, Anthony (2021). Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles. Journal of the European Mathematical Society, 23 (10), 3419-3457. doi: 10.4171/jems/1096
Thermodynamic Formalism for Random Weighted Covering Systems
Atnip, Jason, Froyland, Gary, González-Tokman, Cecilia and Vaienti, Sandro (2021). Thermodynamic Formalism for Random Weighted Covering Systems. Communications in Mathematical Physics, 386 (2), 819-902. doi: 10.1007/s00220-021-04156-1
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
Blachut, Chantelle and González-Tokman, Cecilia (2020). A tale of two vortices: how numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems. Journal of Computational Dynamics, 7 (2), 369-399. doi: 10.3934/JCD.2020015
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
González-Tokman, Cecilia (2018). Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems. Second Meeting Matemáticos Mexicanos en el Mundo [Second meeting of Mexican Mathematicians Abroad], Guanajuato, Mexico, 15-19 December 2014. Guanajuato, Mexico: American Mathematical Society. doi: 10.1090/conm/709/14290
What predictions can I trust? Stability of chaotic random dynamical systems
(2022–2025) ARC Discovery Projects
(2018–2021) University of New South Wales
Coherent structures in chaotic dynamical systems
(2016–2020) ARC Discovery Early Career Researcher Award
Random Dynamical Systems, Transfer Operators and Stability
Doctor Philosophy — Principal Advisor
Other advisors:
(2021) Doctor Philosophy — Principal Advisor
Other advisors:
(2021) 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.