# Stochastic Perturbations to Dynamical Systems: A Response Theory Approach

@article{Lucarini2012StochasticPT, title={Stochastic Perturbations to Dynamical Systems: A Response Theory Approach}, author={Valerio Lucarini}, journal={Journal of Statistical Physics}, year={2012}, volume={146}, pages={774-786} }

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…

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