Upper and lower Hausdorff dimension estimates for invariant sets of k-1-endomorphisms

For a special class of non-injective maps on Riemannian manifolds upper and lower bounds for the Hausdorff dimension of invariant sets are given in te rms of the singular values of the tangent map. The upper estimation is base d on a theorem by DOUADY and OESTERLE and its generalization to Riemannian manifolds by NOACK and REITMANN, but additionally information about the non injectivity is used. The lower estimation can be reached by modifying a met hod, derived by SHERESHEVSKIJ for geometric constructions on the real line (also described by BARREIRA), for similar constructions in general metric s paces. The upper and lower dimension estimates for k-1-endomorphisms can fo r instance be applied to Julia sets of quadratic maps on the complex plane.