38 citations · 143 across the 12 of their papers we have counts for
13 papers
Rigorous and effective numerics for Liverani-Saussol-Vaienti maps
Alexey Korepanov, YuTong Wei, Caroline Wormell
We make highly accurate numerical estimates of basic properties of the invariant measure for Liverani-Saussol-Vaienti intermittent maps, an archetypal slowly mixing dynamical syste…
Highly accurate and fine-scale estimation of equilibrium measures
Caroline L. Wormell
Equilibrium measures are special invariant measures of chaotic dynamical systems and iterated function systems, commonly studied as salient examples of fractal measures. While usef…
A statistical physics and dynamical systems perspective on geophysical extreme events
Davide Faranda, Gabriele Messori, Tommaso Alberti +14
Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and…
Orthogonal polynomial approximation and Extended Dynamic Mode Decomposition in chaos
Caroline L. Wormell
Extended Dynamic Mode Decomposition (EDMD) is a data-driven tool for forecasting and model reduction of dynamics, which has been extensively taken up in the physical sciences. Whil…
On convergence of linear response formulae in some piecewise hyperbolic maps
Caroline L. Wormell
When high-dimensional non-uniformly hyperbolic chaotic systems undergo dynamical perturbations, their long-time statistics are generally observed to respond differentiably with res…
Conditional mixing in deterministic chaos
Caroline L. Wormell
While on the one hand, chaotic dynamical systems can be predicted for all time given exact knowledge of an initial state, they are also in many cases rapidly mixing, meaning that s…
Non-hyperbolicity at large scales of a high-dimensional chaotic system
Caroline L. Wormell
The dynamics of many important high-dimensional dynamical systems are both chaotic and complex, meaning that strong reducing hypotheses are required to understand the dynamics. The…
Efficient computation of statistical properties of intermittent dynamics
Caroline L. Wormell
Intermittent maps of the interval are simple and widely-studied models for chaos with slow mixing rates, but have been notoriously resistant to numerical study. In this paper we pr…
Spectral convergence of diffusion maps: improved error bounds and an alternative normalisation
Caroline L. Wormell, Sebastian Reich
Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of…
Linear response for macroscopic observables in high-dimensional systems
Caroline L. Wormell, Georg A. Gottwald
The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess…
On the validity of linear response theory in high-dimensional deterministic dynamical systems
Caroline L. Wormell, Georg A. Gottwald
This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical lo…
Spectral Galerkin methods for transfer operators in uniformly expanding dynamics
Caroline L. Wormell
Markov expanding maps, a class of simple chaotic systems, are commonly used as models for chaotic dynamics, but existing numerical methods to study long-time statistical properties…
On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series
Georg A. Gottwald, Caroline L. Wormell, Jeroen Wouters
Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-…