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Xue-Mei Li : Stirring the geodesics (Apr 17, 2014 2:55 PM)

In this talk, we discuss stochastic homogeneization on the Hopf fibration. Let us consider Berger's metrics on the three sphere, obtained by shrinking the Hopf circle directions by a factor epsilon. So we think of three spheres as two spheres attached at each point a circle. We consider a particle that is moved by two vector fields: a unit speed vector field, with respect to Berger's metrices, along the Hopf circle; and also a non-zero vector field in` \(S^2\) direction' with speed given by a one dimensional Brownian motion. In the limit of epsilon goes to zero, we obtain a Brownian motion on \(S^2\). The effective motion is obtained by moving a particle along a fast rotating horizontal direction.

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