Hausdorff dimension for non-hyperbolic repellers II: DA diffeomorphisms

Vanderlei Horita; Marcelo Viana

doi:10.3934/dcds.2005.13.1125

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2005, Volume 13, Issue 5: 1125-1152. Doi: 10.3934/dcds.2005.13.1125

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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
2.
IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ

Received: January 31, 2005

Revised: May 31, 2005

Published: September 2005

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Abstract

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.

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Mathematics Subject Classification: Primary: 37C45, 37D25; Secondary: 37C70, 37D30.

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