Stochastic Perturbations to Dynamical Systems: A Response Theory Approach

  title={Stochastic Perturbations to Dynamical Systems: A Response Theory Approach},
  author={Valerio Lucarini},
  journal={Journal of Statistical Physics},
  • V. Lucarini
  • Published 1 March 2011
  • Physics
  • Journal of Statistical Physics
Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that… 
On Some Aspects of the Response to Stochastic and Deterministic Forcings
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Predicting the response of a system to perturbations is a key challenge in mathematical and natural sciences. Under suitable conditions on the nature of the system, of the perturbation, and of the
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  • V. Lucarini
  • Mathematics
    Journal 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.
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Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the
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