Office: | Room 491, Carslaw Building |
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Email: | givenname.surname@sydney.edu.au |

Links: | CV (Sep '23), Google Scholar, PhD thesis |

Numerics for statistical properties of chaotic systems

Data-based operator approximation (Diffusion maps, Dynamic Mode Decompositionâ€¦)

Wormell, C.L., Orthogonal polynomial approximation and Extended Dynamic Mode Decomposition in chaos (2023). Preprint

Wormell, C.L., On convergence of linear response formulae in some piecewise hyperbolic maps (2022). Preprint

Wormell, C.L., Conditional mixing in deterministic chaos. *Ergodic Theory and Dynamical Systems* **44(6)** (2024) 1693-1723. Preprint, DOI

Wormell, C.L., Non-hyperbolicity at large scales of a high-dimensional chaotic system. *Proceedings of the Royal Society B* **478** (2022) 20210808. Preprint, DOI

Wormell, C.L., Efficient computation of statistical properties of intermittent dynamics (2021). Preprint

Wormell, C.L. and Reich, S., Spectral convergence of diffusion maps: improved error bounds and an alternative normalisation. *SIAM Journal of Numerical Analysis* **59(3)** (2021) 1687–1734. Preprint, DOI

Wormell, C.L. and Gottwald, G.A., Linear response for macroscopic observables in high-dimensional systems. *Chaos* **29(11)** (2019) 113127. Preprint, DOI

Wormell, C.L., Spectral Galerkin methods for transfer operators in uniformly expanding dynamics. *Numerische Mathematik* **14** (2019) 421–463.
Preprint, DOI

Wormell, C.L. and Gottwald, G.A., On the validity of linear response theory in high-dimensional deterministic dynamical systems. *Journal of Statistical Physics* **172(6)** (2018) 1479–1498. Preprint, DOI

Gottwald, G.A., Wormell, C.L., and Wouters, J.,
On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series.
*Physica D*
**331** (2016) 89–101. Preprint, DOI

Minicourse on *spectral theory and approximation of Koopman operators in chaos*. Data-driven Dynamical Systems summer school, Bremen (Jul 2024). Slides 1 2 3

*Polynomial discretisations of transfer and Koopman operators in chaotic dynamics*. Presentation at ICIAM 2023, Tokyo (Aug 2023). Slides

Minicourse on *numerical methods in (non-hyperbolic) chaos*. Statistical and Computational Aspects of Dynamical Systems, Pisa (Dec 2022). Slides: 1 2 3 4

*Prediction from perfect partial observations and linear response*. Presentation at Modern Mathematics for Complex Systems, London (Jun 2022) Slides, video

*Conditional decay of correlations and linear response*. Presentation at Geometry of Deterministic and Random Fractals, Budapest (Jun 2022) Slides

*Linear response in higher dimensions and mixing of Cantor sets*. Talk at AustMS 2021 (Dec 2021). Slides

*Applications of Chebyshev transfer operator methods*. Invited talk at Rencontre ANR Aléatoire, Dynamique et Spectre, Nantes (Nov 2021). Slides

*Linear response for piecewise hyperbolic maps and mixing of SRB measure cross-sections*. Seminar at Ergodic Theory and Dynamical Systems colloquium, Warwick University (Nov 2021).

*Linear response in high-dimensional globally coupled systems*. Online seminar for WG Climate & Statistical Mechanics, Université d'Orsay (Oct 2021).

*Non-hyperbolicity in large-scale dynamics of high-dimensional chaotic systems*. Online seminar for Queen Mary University of London Complex Systems seminar (Oct 2021).

*Operator convergence of diffusion maps and the bistochastic normalisation*. Talk at On Future Synergies for Stochastic and Learning Algorithms, CIRM Luminy (Sep 2021). Slides

*Macroscopic dynamics of globally coupled systems*. Talk at Second Workshop on Wild Dynamics, São Miguel, Azores, Portugal (Sep 2021). Slides

*Emergence and breakdown of linear response in globally coupled systems*. Talk at International Conference on Mathematical Physics, Geneva (Aug 2021). Slides, Video

*Linear response for the Lozi map and mixing of SRB measure cross-sections*. Talk at École d'été finistérienne en systèmes dynamiques, Brest (Jun 2021).

*Operator convergence of diffusion maps and the bistochastic normalisation*. Talk at SIAM Conference on Applications of Dynamical Systems, online (May 2021). Slides

*Linear response in high-dimensional globally coupled chaotic dynamics*. Seminar at Courant Networks and Dynamical Systems, online (Apr 2021).

*Rigorously validated estimation of statistical properties of expanding
maps*. Talk at AMS Spring Southeastern Sectional Meeting, online (Mar 2021).

*Linear response in high-dimensional globally coupled systems*. Invited talk at Linear Response: Rigorous Results and Applications, online (Jan 2021). Slides, video

*Rigorously validated estimation of statistical properties of expanding maps*. Seminar at CRM-CAMP, online (Aug 2020). Slides

*Spectral convergence of diffusion maps.* Seminar at Sydney Dynamics Group, online (Jun 2020). Slides

*Spectral Galerkin transfer operator methods in uniformly-expanding dynamics.* Seminar at Georgia Tech CDSNS Colloquium, online (Jun 2020). Slides

*Linear response for macroscopic observables in high-dimensional systems.*
Invited talk at Multiscale Methods for Deterministic and Stochastic Dynamics, Geneva (Jan 2020). Slides

*Linear response for macroscopic observables in high-dimensional systems.*
Invited talk at Response theory and its applications in geophysical fluid dynamics, Institut Henri Poincaré (Oct 2019). Slides

*Emergence of linear response at macroscopic scales.* Poster at Nonlinear and stochastic methods in climate and geophysical fluid dynamics, Institut Henri Poincaré (Oct 2019). Poster