We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations. For comparison,...

The local deformations of a submanifold under the effect of a smooth dynamical system are studied with the help of Oseledets’ multiplicative ergodic theorem. Equivalence classes of submanifolds, called jets, are introduced in order to describe these local deformations. They identify submanifolds having the same approximations up to some order at a given point. For every order $k$, a condition on the Lyapunov exponents of the dynamical system is established insuring the convergence of the $k$-jet of...