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.
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