Hausdorff Dimension for Non-Hyperbolic Repellers II: DA Diffeomorphisms

Marcelo Viana | Horita, Vanderlei

Keywords: Hausdorff dimension | limit capacity | repeller | DA diffeomorphism

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by M. Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

Anexos:

• hv2.pdf