# Linear response, susceptibility and resonances in chaotic toy models

@article{Cessac2007LinearRS, title={Linear response, susceptibility and resonances in chaotic toy models}, author={Bruno Cessac and Jacques-A. Sepulchre}, journal={Physica D: Nonlinear Phenomena}, year={2007}, volume={225}, pages={13-28} }

## 41 Citations

### Fluctuation Relations and Nonequilibrium Response for Chaotic Dissipative Dynamics

- Physics
- 2013

In a recent paper [Colangeli and Rondoni, Physica D 241:681, 2011] it was argued that the Fluctuation Relation for the phase space contraction rate Λ could suitably be extended to non-reversible…

### Beyond the linear fluctuation-dissipation theorem: the role of causality

- Physics
- 2012

In this paper we tackle the traditional problem of relating the fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also…

### Fluctuation-dissipation relation for chaotic non-Hamiltonian systems

- Physics
- 2012

In dissipative dynamical systems phase space volumes contract, on average. Therefore, the invariant measure on the attractor is singular with respect to the Lebesgue measure. As noted by Ruelle, a…

### Handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics.

- PhysicsPhysical review. E
- 2021

A general formulation of the fluctuation-dissipation relations (FDRs) holding also in far-from-equilibrium stochastic dynamics, and allows to reproduce, in a suitable small-noise limit, the response functions of deterministic, strongly nonlinear dynamical models, even in the presence of chaotic behavior.

### Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

- Physics
- 2017

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant…

### Crisis of the chaotic attractor of a climate model: a transfer operator approach

- Physics
- 2015

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are known to be characterised by a single or a pair of…

### On Some Aspects of the Response to Stochastic and Deterministic Forcings

- Physics
- 2022

The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. In the case of background…

### Revising and Extending the Linear Response Theory for Statistical Mechanical Systems: Evaluating Observables as Predictors and Predictands

- MathematicsJournal of Statistical Physics
- 2018

The rigid separation between forcing and response is broken, which is key in linear response theory, and the concept of causality is revisited, finding that not all observables are equally good as predictors when a given forcing is applied.

### Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems

- Mathematics, PhysicsJournal of statistical physics
- 2014

It is derived that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds.

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