Fers à cheval non uniformément hyperboliques engendrés par une bifurcation homocline et densité nulle des attracteurs

Jean-Christophe Yoccoz | Palis, Jacob

Keywords: fers à cheval | hyperbolicité | non uniforme | bifurcation homocline | attracteurs

We consider the unfolding of the homoclinic tangency associated to a periodic point, which is part of a horseshoe (hyperbolic set) on a surface. By previous results of Newhouse-Palis and Palis-Takens hyperbolicity prevails at the bifurcation parameters in the Hausdorff dimension of the horseshoe is smaller than one. In the present paper we show that even in the case where the Hausdorff dimension is bigger than one but, not much bigger, a kind of hyperbolicity prevails, the so called non-uniform one. In particular, attractors having density zero at the initial value of the unfolding.

Anexos:

• yoccoz.pdf