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October  2005, 13(5): 1125-1152. doi: 10.3934/dcds.2005.13.1125

Hausdorff dimension for non-hyperbolic repellers II: DA diffeomorphisms

Vanderlei Horita 1, and  Marcelo Viana 2,

1. 

Departamento de Matemática, IBILCE/UNESP, Rua Cristóvão Colombo, 2265, 15055-S. J. Rio Preto, SP, Brazil
2. 

IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ, Brazil

Received  February 2005 Revised  June 2005 Published  September 2005

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 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.
Keywords: Repeller., Dimension theory, Non-uniform hyperbolicity.
Mathematics Subject Classification: Primary: 37C45, 37D25; Secondary: 37C70, 37D3.
Citation: Vanderlei Horita, Marcelo Viana. Hausdorff dimension for non-hyperbolic repellers II: DA diffeomorphisms. Discrete and Continuous Dynamical Systems, 2005, 13 (5) : 1125-1152. doi: 10.3934/dcds.2005.13.1125
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