activity
20162026
most citedLinear response for macroscopic observables in high-dimensional systems

38 citations · 143 across the 12 of their papers we have counts for

collaborators

13 papers

math.DS2026

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…

math.DS2023

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…

physics.ao-ph2023★ 1 cited

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…

math.NA2023

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…

math.DS2022★ 2 cited

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…

math.DS2022★ 7 cited

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…

nlin.CD2021

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…

math.DS2021

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…

math.ST2020★ 12 cited

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…

math.DS2019★ 38 cited

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…

math.DS2018★ 33 cited

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…

math.DS2017★ 23 cited

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…

nlin.CD2016★ 27 cited

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-…