# Gaussian perturbations of circle maps: A spectral approach

@article{Mayberry2009GaussianPO, title={Gaussian perturbations of circle maps: A spectral approach}, author={J. P. Mayberry}, journal={Annals of Applied Probability}, year={2009}, volume={19}, pages={1143-1171} }

In this work, we examine spectral properties of Markov transition operators corresponding to Gaussian perturbations of discrete time dynamical systems on the circle. We develop a method for calculating asymptotic expressions for eigenvalues (in the zero noise limit) and show that changes to the number or period of stable orbits for the deterministic system correspond to changes in the number of limiting modulus 1 eigenvalues of the transition operator for the perturbed process. We call this…

## 2 Citations

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