## Abstract

We study the small mass limit of the equation describing planar motion of a charged particle of a small mass µ in a force field, containing a magnetic component, perturbed by a stochastic term. We regularize the problem by adding a small friction of intensity ǫ > 0. We show that for all small but fixed frictions the small mass limit of q_{µ,ǫ} gives the solution q_{ǫ} to a stochastic first order equation, containing a noise-induced drift term. Then, by using a generalization of the classical averaging theorem for Hamiltonian systems by Freidlin and Wentzell, we take the limit of the slow component of the motion q_{ǫ} and we prove that it converges weakly to a Markov process on the graph obtained by identifying all points in the same connected components of the level sets of the magnetic field intensity function.

Original language | English (US) |
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Journal | Unknown Journal |

State | Published - Mar 4 2020 |

## ASJC Scopus subject areas

- General