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We consider randomly forced 2D Navier-Stokes equations in a bounded domain with smooth boundary. It is assumed that the random perturba- tion is non-degenerate, and its law is periodic in time and has a support localised with respect to space and time. Concerning the unperturbed problem, we assume that it is approximately controllable in infinite time by an external force whose support is included in that of the random force. Under these hypotheses, we prove that the Markov process generated by the restriction of solutions to the instants of time proportional to the period possesses a unique stationary distribution, which is exponentially mixing. The proof is based on a coupling argument, a local controllability property of the Navier-Stokes system, an estimate for the total variation distance between a measure and its image under a smooth mapping, and some classical results from the theory of optimal transport., Comment: 30 pages

We introduce the notion of the dynamical length of an invariant arc of a rational map R. A pinching deformation is a sequence of topological deformations of R such that the corresponding dynamical length shrinks to zero. We show that if the sequence converges to a rational map then the spherical diameter of the corresponding arc also shrinks to zero. We use this result to show that if the grand orbits of the closure of finitely many such arcs separate the Julia set, the deformations of R diverge. This is a generalization of a result stated by P. Makienko but with a different approach. We also present a rich collection of examples.  2002 Editions scientifiques et medicales Elsevier SAS