Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

Edge states in the climate system: exploring global instabilities and critical transitions

(2017) Valerio Lucarini et al.   NONLINEARITY

Fluctuations, response, and resonances in a simple atmospheric model

(2017) Andrey Gritsun et al.   PHYSICA D-NONLINEAR PHENOMENA

Global Stability Analysis Using the Eigenfunctions of the Koopman Operator

(2016) Alexandre Mauroy et al.   IEEE TRANSACTIONS ON AUTOMATIC CONTROL

The Quest for the Ultimate Anisotropic Banach Space

(2016) Viviane Baladi   JOURNAL OF STATISTICAL PHYSICS

Alignment of Lyapunov Vectors: A Quantitative Criterion to Predict Catastrophes?

(2016) Marcus W. Beims et al.   Scientific Reports

An early warning indicator for atmospheric blocking events using transfer operators

(2015) Alexis Tantet et al.   CHAOS

A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

(2015) Matthew O. Williams et al.   JOURNAL OF NONLINEAR SCIENCE

Response Operators for Markov Processes in a Finite State Space: Radius of Convergence and Link to the Response Theory for Axiom A Systems

(2015) Valerio Lucarini   JOURNAL OF STATISTICAL PHYSICS

On using extreme values to detect global stability thresholds in multi-stable systems: The case of transitional plane Couette flow

(2014) Davide Faranda et al.   CHAOS SOLITONS & FRACTALS

Global instability in the Ghil–Sellers model

(2014) Tamás Bódai et al.   CLIMATE DYNAMICS

Statistical early-warning indicators based on autoregressive moving-average models

(2014) Davide Faranda et al.   Journal of Physics A-Mathematical and Theoretical

Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances

(2014) Mickaël David Chekroun et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Understanding Chaotic Dynamical Systems

(2013) Lai-Sang Young   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

On the relation between Lyapunov exponents and exponential decay of correlations

(2013) Julia Slipantschuk et al.   Journal of Physics A-Mathematical and Theoretical

Estimating Long-Term Behavior of Flows without Trajectory Integration: The Infinitesimal Generator Approach

(2013) Gary Froyland et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Theory and Computation of Covariant Lyapunov Vectors

(2012) Pavel V. Kuptsov et al.   JOURNAL OF NONLINEAR SCIENCE

Stochastic Perturbations to Dynamical Systems: A Response Theory Approach

(2012) Valerio Lucarini   JOURNAL OF STATISTICAL PHYSICS

Linearization in the large of nonlinear systems and Koopman operator spectrum

(2012) Yueheng Lan et al.   PHYSICA D-NONLINEAR PHENOMENA

On Malliavinʼs proof of Hörmanderʼs theorem

(2011) Martin Hairer   BULLETIN DES SCIENCES MATHEMATIQUES

Lyapunov statistics and mixing rates for intermittent systems

(2011) Carlos J. A. Pires et al.   PHYSICAL REVIEW E

Early warning of climate tipping points

(2011) Timothy M. Lenton   Nature Climate Change

A simple framework to justify linear response theory

(2010) Martin Hairer et al.   NONLINEARITY

Anasazi software for the numerical solution of large-scale eigenvalue problems

(2009) C. G. Baker et al.   ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE

Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System

(2009) Valerio Lucarini   JOURNAL OF STATISTICAL PHYSICS

Data-Based Inference of Generators for Markov Jump Processes Using Convex Optimization

(2009) Daan Crommelin et al.   MULTISCALE MODELING & SIMULATION

Early-warning signals for critical transitions

(2009) Marten Scheffer et al.   NATURE

A review of linear response theory for general differentiable dynamical systems

(2009) David Ruelle   NONLINEARITY

Hyperbolicity and the Effective Dimension of Spatially Extended Dissipative Systems

(2009) Hong-liu Yang et al.   PHYSICAL REVIEW LETTERS

Lyapunov Measure for Almost Everywhere Stability

(2008) Umesh Vaidya et al.   IEEE TRANSACTIONS ON AUTOMATIC CONTROL