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}
}

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References

SHOWING 1-10 OF 24 REFERENCES

Numerical evidence of linear response violations in chaotic systems

It has been rigorously shown in [11] that the complex susceptibility for chaotic maps of the interval can have a pole in the upper complex plane. I develop a numerical procedure allowing to exhibit

Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics

This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics. We adopt a new point of view which has emerged

Stable resonances and signal propagation in a chaotic network of coupled units.

This dynamic differentiation, induced by nonlinearities, exhibits the different ability that units have to transmit a signal in this network of nonlinearly interacting units.

Transmitting a signal by amplitude modulation in a chaotic network

How the dynamics may interfere with the graph topology to produce an effective transmission network, whose topology depends on the signal, and cannot be directly read on the "wired" network is discussed.

Field driven thermostated systems: A nonlinear multibaker map

In this paper we discuss a simple deterministic model for a field driven, thermostated random walk that is constructed by a suitable generalization of a multibaker map. The map is a usual multibaker,

Linear response of the Lorenz system.

  • C. Reick
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
The present results indicate that in contrast to a recent speculation the large system limit (thermodynamic limit) need not be invoked to obtain a linear response for chaotic systems of this type.

An introduction to chaos in nonequilibrium statistical mechanics

Preface 1. Non-equilibrium statistical mechanics 2. The Boltzmann equation 3. Liouville's equation 4. Poincare recurrence theorem 5. Boltzmann's ergodic hypothesis 6. Gibbs' picture-mixing systems 7.

Brownian Motion and Nonequilibrium Statistical Mechanics

The fluctuation-dissipation theorem, which states that irreversible processes ip nonequilibrium are necessarily related to thermal fluctuations in equilibrium, is described and the meaning of stochastization is considered.