Cecilia González Tokman

cecilia.gt uq . edu . au
School of Mathematics and Physics
The University of Queensland
St Lucia, QLD 4072

Building 67 (Priestley)
Room 545
+61 (7) 3365-3271
Welcome! I am a senior lecturer (ARC DECRA Fellow) at the School of Mathematics and Physics at The University of Queensland.
My research interests are in Dynamical Systems and Ergodic Theory: applied, theoretical and numerical aspects.

Upcoming and recent events

I am co-organising the fourth meeting of Mexican Mathematicians in the World (Matemáticos Mexicanos en el Mundo) at Casa Matemática Oaxaca (CMO, June 10-15, 2018).


(Preprint versions may differ slightly from published versions.)
  • Hilbert space Lyapunov exponent stability, (joint with G. Froyland and A. Quas).
    Transactions of the American Mathematical Society, to appear.
    [ arXiv ]
  • Almost sure invariance principle for random piecewise expanding maps, (joint with D. Dragičević, G. Froyland and S. Vaienti).
    Nonlinearity, to appear.
    [ arXiv ]
  • A spectral approach for quenched limit theorems for random expanding dynamical systems, (joint with D. Dragičević, G. Froyland and S. Vaienti).
    Communications in Mathematical Physics, to appear.
    [ arXiv ]
  • Quenched stochastic stability for eventually expanding-on-average random interval map cocycles, (joint with G. Froyland and R. Murray).
    Ergodic Theory and Dynamical Systems, to appear.
    [ pdf ]
  • Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems.
    Contemporary Mathematics, to appear.
    [ pdf ]
  • Optimal mixing enhancement by local perturbation, (joint with G. Froyland and T. Watson).
    SIAM Review, 58(3): 494-513, 2016.
    [ pdf | journal ]
  • Stochastic stability of Lyapunov exponents and Oseledets splittings for semi-invertible matrix cocycles, (joint with G. Froyland and A. Quas).
    Communications on Pure and Applied Mathematics, 68: 2052-2081, 2015.
    [ pdf | journal ]
  • A concise proof of the Multiplicative Ergodic Theorem on Banach spaces, (joint with A. Quas).
    Journal of Modern Dynamics, 9: 237-255, 2015.
    [ pdf | journal ]
  • Stability and approximation of invariant measures of Markov chains in random environments, (joint with G. Froyland).
    Stochastics and Dynamics, 16(1):1650003, 2016.
    [ pdf | journal ]
  • Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools, (joint with A. Quas and G. Froyland).
    Journal of Computational Dynamics, Pages: 249 - 278, Volume 1, Issue 2, December 2014.
    [ pdf | journal | bibtex ]
  • Ulam's method for Lasota-Yorke maps with holes, (joint with C. Bose, G. Froyland and R. Murray).
    SIAM Journal on Applied Dynamical Systems, 2014, 13:2, 1010-1032.
    [ pdf | journal | bibtex ]
  • Stability and approximation of random invariant densities for Lasota-Yorke map cocycles, (joint with G. Froyland and A. Quas).
    Nonlinearity, 27 (2014) 647-660.
    [ pdf | journal | bibtex ]
  • A semi-invertible operator Oseledets theorem, (joint with A. Quas).
    Ergodic Theory and Dynamical Systems, 34 (2014), 1230-1272.
    [ pdf | journal | bibtex ]
  • Ensemble data assimilation for hyperbolic systems, (joint with B. Hunt).
    Physica D: Nonlinear Phenomena, Volume 243, Issue 1, 15 January 2013, 128-142.
    [ pdf | journal | bibtex ]
  • Approximating invariant densities for metastable systems, (joint with B. Hunt and P. Wright).
    Ergodic Theory and Dynamical Systems, 31 (2011), 1345-1361.
    [ pdf | journal | bibtex | poster ]
  • Scaling laws for bubbling bifurcations, (joint with B. Hunt).
    Nonlinearity 22 (2009), 2607-2631.
    [ pdf | journal | bibtex ]

Other works

  • Multiplicative ergodic theorems and applications. (joint with A. Quas).
    CMS Notes, Volume 45 No. 5, October/ November 2013, 14-15. (Canadian Mathematical Society official newsletter).
    [ pdf | CMS Notes ]


  • Current students
    • F. Batayneh, PhD student.
    • C. Blachut, PhD student.
  • Former students
    • Peter Cudmore, PhD 2017, UQ.
    • Hayden Hohns, Hons 2016, UQ.
    • Lachlan Burton, Summer Research Scholar 2015-2016, UQ.
    • Cale Rankin, Summer Research Scholar 2015-2016, UQ.
    • Jeremy Nugent, Hons 2014, UNSW, (jointly supervised with G. Froyland).
    • Georgia Tsambos, Hons 2013, UNSW, (jointly supervised with G. Froyland).
If you are interested in discussing possible research projects (e.g. honours, PhD) in the areas of Dynamical Systems and Ergodic Theory, feel free to send me an email, including the following: (i) a few words about your research interests; (ii) your CV/transcripts; and (iii) samples of your written work, such as any papers, theses and/or senior/honours projects, if applicable.

Teaching activities

  • Current/Upcoming courses at UQ
    • Semester 1, 2018. Math 3101: Bifurcations and Chaos (UQ).
      Consultation hours: Wednesday, Thursday 10-11 am.
      Course material, assignments and other resources are available to enrolled students via Learn.UQ.
  • Previous courses
    • Semester 1, 2017. Math 1051: Calculus and Linear Algebra (UQ).
    • Semester 1, 2016. Math 3101: Bifurcations and Chaos (UQ).
    • Semester 2, 2015. Math 4104: Advanced Hamiltonian Dynamics and Chaos (UQ).
    • Semester 2, 2014. Math 5175: Ergodic Theory, Dynamical Systems and Applications (UNSW).
    • Semester 1, 2014. Math 1031: Mathematics for Life Sciences (UNSW).
    • Fall 2011. Math 300: Advanced Calculus (University of Victoria).
    • Fall 2010. Math 151: Finite Mathematics (University of Victoria).

Events co-organised

Dynamical Systems and Fluid Dynamics Special Session at the WIMSIG Conference, 24-26 Sep 2017, University of South Australia.  
Mathsfest Workshop "Advances in Ergodic Theory, Hyperbolic Dynamics and Statistical Laws", Nov-Dec 2016, The Australian National University. 3rd meeting of Mexican mathematicians (Tercera Reunión de Matemáticos Mexicanos en el Mundo), 15-19 August 2016, CIMAT, Mexico.
Workshop on Random Dynamical Systems and Multiplicative Ergodic Theorems, 18-23 January 2015, BIRS, Banff, Canada. Dynamical Systems Special Session at the 59th Annual Meeting of the Australian Mathematical Society, September 28 - October 1st, 2015, Flinders University, Adelaide.
Focused Research Group on Ergodic Theory and Transfer Operators, 12-16 August 2013, CIMAT, Guanajuato, Mexico. International Workshop on Set-Oriented Numerics in Dynamical Systems, 3-6 September 2012, UNSW, Sydney.