Perturbation theory for the Fokker-Planck operator in chaos
arXiv:1602.03044 · doi:10.1016/j.cnsns.2017.06.025
Abstract
The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this situation. In contrast, the presence of additive noise smooths out the stationary distribution, and perturbation theory becomes applicable. We show that a perturbation expansion for the Fokker-Planck evolution operator yields surprisingly accurate estimates of long-time averages in an otherwise unlikely scenario.
arXiv comment16 pages, 8 figures
References in corpus (9)
- The Moore-Penrose Pseudoinverse. A Tutorial Review of the Theory
- A review of linear response theory for general differentiable dynamical systems
- Dynamic Algorithm for Parameter Estimation and Its Applications
- Linear response, or else
- On Determining the Eigenprojection and Components of a Matrix
- How well can one resolve the state space of a chaotic map?
- Continuity properties of transport coefficients in simple maps
- Knowing when to stop: how noise frees us from determinism
- Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system