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May  2006, 15(2): 481-504. doi: 10.3934/dcds.2006.15.481

Basin problem for Hénon-like attractors in arbitrary dimensions

Vanderlei Horita 1, and  Nivaldo Muniz 2,

1. 

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

Departamento de Matemática, UFMA, Avenida dos Portugueses, S/N, 65000-000 São Luís, MA, Brazil

Received  May 2005 Revised  October 2005 Published  March 2006

We prove that Hénon-like strange attractors of diffeomorphisms in any dimensions, such as considered in [2], [7], and [9] support a unique Sinai-Ruelle-Bowen (SRB) measure and have the no-hole property: Lebesgue almost every point in the basin of attraction is generic for the SRB measure. This extends two-dimensional results of Benedicks-Young [4] and Benedicks-Viana [3], respectively.
Keywords: Hénon-like attractor, non-uniformly hyperbolic system, SRB measure..
Mathematics Subject Classification: Primary: 37D45; Secondary: 37C40, 37D25, 37E9.
Citation: Vanderlei Horita, Nivaldo Muniz. Basin problem for Hénon-like attractors in arbitrary dimensions. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 481-504. doi: 10.3934/dcds.2006.15.481
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