Linear response, or else

By Viviane Baladi. 2014

121 citations recorded by the source corpus.

Consider a smooth one-parameter family t ! ft of dynamical systems ft, with |t| < ϵ. Assume that for all t (or for many t close to t =0 ) the map ft admits a unique physical invariant probability measure µt. We say that linear response holds if t ! µt is differentiable at t =0 (possibly in the sense of Whitney), and if its derivative can be expressed as a function of f0, µ0, and ∂tft|t=0. The goal of this note is to present to a general mathematical audience recent results and open problems in the theory of linear response for chaotic dynamical systems, possibly with bifurcations.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c16914ce82dc8b628565cdd177c7a088ffbd9783

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Valerio Lucarini
2. Francesco Ragone
3. F. Lunkeit

In Statistical and Nonlinear Physics

1. Valerio Lucarini
2. Francesco Ragone
3. F. Lunkeit
4. Michael Ghil

Citations in the corpus

• Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns (2015, background): “In other terms, the focus is on studying directly how the invariant measure changes as a result of the applied perturbation and the challenge is in finding appropriate mathematical embedding in terms of suitable functional spaces [104, 105, 43, 106].”