Basin problem for Hénon-like attractors in arbitrary dimensions

Vanderlei Horita; Nivaldo Muniz

doi:10.3934/dcds.2006.15.481

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2006, Volume 15, Issue 2: 481-504. Doi: 10.3934/dcds.2006.15.481

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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

Received: April 30, 2005

Revised: September 30, 2005

Published: March 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 37D45; Secondary: 37C40, 37D25, 37E99.

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