Overview
Background
Cecilia is an associate professor in the School of Mathematics and Physics at the University of Queensland. After completing undergraduate studies at Universidad de Guanajuato / CIMAT and PhD at the University of Maryland, College Park, she held research fellowships from the Pacific Institute for the Mathematical Sciences (PIMS) and the Australian Research Council (ARC). She has also held a Promoting Women Fellowship by UQ.
Cecilia is an expert in the field of random dynamical systems (RDS). Along with collaborators, she has developed a framework for the study of transport in RDS, relying on the so-called Lyapunov–Oseledets spectrum. Her key contributions include the development of tools and algorithms to (i) approximate coherent structures and Lyapunov exponents, (ii) establish limit laws and quantify fluctuations, (iii) develop a thermodynamic formalism and (iv) optimise mixing. Her work also includes significant advances on data assimilation, metastable and dynamical systems.
Cecilia has received significant research funding from the Australian Research Council, including a 2016 Discovery Early Career Researcher Award (DECRA) a 2018 ARC DP and a 2022 ARC DP as lead CI. She has led or co-led competitive applications for conference funding (20-60 participants), including a 2023 MATRIX Workshop, co-funded by the MATRIX-Simons Collaborative Fund, an Australian Mathematical Sciences Institute (AMSI) funded Mathsfest Workshop (ANU, 2016), a Banff International Research Station Workshop (Canada, 2015) and a BIRS-CMO Workshop (Mexico, 2018).
Cecilia has delivered over a hundred invited lectures, seminars and colloquia in almost twenty countries, including invited/keynote addresses at the ANZIAM 2023 annual conference, 2014 International Workshop Set Oriented Numerics (U Canterbury, NZ), 2017 Workshop Ergodic Theory, Algorithms & Rigorous Computations (U Warwick, UK), 2017 EMALCA (Latin-American & Caribbean Math School, Mexico) and participation at invitation-only workshops at AIM (USA), BIRS (Canada), Bernoulli Center (Switzerland), CMO (Mexico), CIRM (France), Centro De Giorgi (Italy), Lorentz Center (Netherlands) and MATRIX (Australia).
Cecilia's service roles include: MATRIX Scientific Committee (2019-), Australian Mathematical Society council (2018-2021) and Queensland representative at the ANZIAM Executive Committee (2019-2021).
Availability
- Associate Professor Cecilia Gonzalez Tokman is:
- Available for supervision
Fields of research
Research interests
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Dynamical Systems and Ergodic Theory
Cecilia’s research interests include dynamical systems, ergodic theory and related areas. Her recent work focuses on random dynamical systems, transfer operators, Lyapunov exponents and coherent structures.
Works
Search Professor Cecilia Gonzalez Tokman’s works on UQ eSpace
Featured
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
Featured
2018
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
Featured
2016
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
Featured
2015
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
2024
Journal Article
Prevalence of stability for smooth Blaschke product cocycles fixing the origin
Gonzalez-Tokman, Cecilia and Peters, Joshua (2024). Prevalence of stability for smooth Blaschke product cocycles fixing the origin. Discrete and Continuous Dynamical Systems. doi: 10.3934/dcds.2024104
2023
Journal Article
A patch in time saves nine: methods for the identification of localised dynamical behaviour and lifespans of coherent structures
Blachut, Chantelle, González-Tokman, Cecilia and Hernández-Dueñas, Gerardo (2023). A patch in time saves nine: methods for the identification of localised dynamical behaviour and lifespans of coherent structures. Journal of Nonlinear Science, 33 (4) 55. doi: 10.1007/s00332-023-09911-3
2022
Journal Article
Shifts in evolutionary balance of phenotypes under environmental changes
Kleshnina, Maria, McKerral, Jody C., González-Tokman, Cecilia, Filar, Jerzy A. and Mitchell, James G. (2022). Shifts in evolutionary balance of phenotypes under environmental changes. Royal Society Open Science, 9 (11) 220744, 1-17. doi: 10.1098/rsos.220744
2022
Journal Article
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, 43 (10) PII S0143385722000682, 3193-3215. doi: 10.1017/etds.2022.68
2022
Journal Article
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
2022
Journal Article
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
2021
Book
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
2021
Journal Article
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
2021
Journal Article
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
2021
Book Chapter
Preface
Galaz-García, Fernando, González-Tokman, Cecilia and Millán, Juan Carlos Pardo (2021). Preface. Mexican mathematicians in the world: trends and recent contributions. (pp. vii-viii) Providence, RI, United States: American Mathematical Society.
2020
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
2020
Journal Article
A tale of two vortices: how numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems
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
2019
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
2019
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
Journal Article
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
2018
Conference Publication
Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems
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
Supervision
Availability
- Associate Professor Cecilia Gonzalez Tokman is:
- Available for supervision
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Available projects
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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.
Supervision history
Current supervision
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Doctor Philosophy
Random Dynamical Systems, Transfer Operators and Stability
Principal Advisor
Other advisors: Dr Meagan Carney
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Doctor Philosophy
Global stability of chaotic random dynamical systems
Principal Advisor
Other advisors: Dr Meagan Carney
Completed supervision
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2021
Doctor Philosophy
Existence, ergodic properties, and number of random invariant measures for multidimensional quenched random dynamical systems
Principal Advisor
Other advisors: Dr Dietmar Oelz
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2021
Doctor Philosophy
Seeking earthly measures: Algorithms for the detection, tracking and investigation of coherent structures in non-autonomous dynamical systems
Principal Advisor
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2017
Doctor Philosophy
Synchronisation of Nanomechanical Oscillators
Principal Advisor
Other advisors: Professor Joseph Grotowski
Media
Enquiries
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