Math @ Duke

Publications [#328808] of Jonathan C. Mattingly
search arxiv.org.Papers Published
 Bakhtin, Y; Hurth, T; Lawley, SD; Mattingly, JC, Smooth invariant densities for random switching on the torus,
Nonlinearity, vol. 31 no. 4
(April, 2018),
pp. 13311350 [doi]
(last updated on 2018/11/20)
Abstract: We consider a random dynamical system obtained by switching between the flows
generated by two smooth vector fields on the 2dtorus, 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.


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