Witness George transfix the caustic

We will continue discussion of caustics and complex paths, based on exercises by Joseph Keller.

Prof. Keller gave Predrag two problems he uses to familiarize his students with complex phase space trajectories. I will attempt to discuss them this journal club.

(see the paper)

In the presence of white noise in a dynamical system, the delta-shaped core of the Perron-Frobenius operator becomes a Gaussian. For a noisy one-dimensional map or flow with a single fixed point, it is possible to find the eigenspectrum and an invariant measure of such operator analytically. In two dimensions, a noisy cicular limit cycle is discussed.