Random perturbations of codimension one homoclinic tangencies in dimension 3

Adding small random parametric noise to an arc of diffeomorphisms of a manifold of dimension 3, generically unfolding a codimension one quadratic homoclinic tangency q associated to a sectionally dissipative saddle fixed point p , we obtain not more than a finite number of 'physical' probability measures, whose ergodic basins cover the orbits which are recurrent to a neighbourhood of the tangency point q . This result is in contrast to the extension of Newhouse's phenomenon of coexistence of infinitely many sinks obtained by Palis and Viana in this setting. There is a similar result for the simpler bidimensional case whose proof relies on geometric arguments. We now extend the arguments to cover three-dimensional manifolds.