Affiliation:
1. Department of Mathematics, Superior Normal School of Bucharest, IMAR, Cam. 602 Calea Grivitei nr. 21, Bucuresti, Sector 1, Romania
Abstract
Abstract
We study the Hausdorff dimension of the intersection between local stable manifolds and the respective basic sets of a class of hyperbolic polynomial endomorphisms on the complex projective space ℙ2. We consider the perturbation (z
2 +ɛz +bɛw
2, w
2) of (z
2, w
2) and we prove that, for b sufficiently small, it is injective on its basic set Λɛ close to Λ:= {0} × S
1. Moreover we give very precise upper and lower estimates for the Hausdorff dimension of the intersection between local stable manifolds and Λɛ, in the case of these maps.