Random perturbations of codimension one homoclinic tangencies in dimension 3
Dynamical Systems
2007-05-23 v1
Abstract
Adding small random parametric noise to an arc of diffeomophisms 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 neighborhood of the tangency point . 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.
Keywords
Cite
@article{arxiv.math/0204266,
title = {Random perturbations of codimension one homoclinic tangencies in dimension 3},
author = {Vitor Araujo},
journal= {arXiv preprint arXiv:math/0204266},
year = {2007}
}
Comments
22 pages; 5 figures