Duke Applied Mathematics

Publications [#328808] of Jonathan C. Mattingly

Papers Published

1. Bakhtin, Y; Hurth, T; Lawley, SD; Mattingly, JC, Smooth invariant densities for random switching on the torus, vol. 31 no. 4 (August, 2017), pp. 1331-1350, IOP Publishing [doi]
   (last updated on 2024/04/18)

   Abstract:
   We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the driving vector fields are transversal to each other at all points of the torus and that each of them allows for a smooth invariant density and no periodic orbits, we prove that the switched system also has a smooth invariant density, for every switching rate. Our approach is based on an integration by parts formula inspired by techniques from Malliavin calculus.