Dynamical properties of singular-hyperbolic attractors

Aubin Arroyo; Enrique R. Pujals

doi:10.3934/dcds.2007.19.67

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2007, Volume 19, Issue 1: 67-87. Doi: 10.3934/dcds.2007.19.67

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Dynamical properties of singular-hyperbolic attractors

Aubin Arroyo^1, and
Enrique R. Pujals^2,

1.
UNAM - Instituto de Matemáticas, U. Cuernavaca, A.P. 273 Admon. de correos # 3, Cuernavaca, Morelos 62251, México
2.
IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro

Received: July 31, 2005

Revised: March 31, 2007

Published: December 2006

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Abstract

We provide a dynamical portrait of singular-hyperbolic transitive attractors of a flow on a 3-manifold. Our Main Theorem establishes the existence of unstable manifolds for a subset of the attractor which is visited infinitely many times by a residual subset. As a consequence, we prove that the set of periodic orbits is dense, that it is the closure of a unique homoclinic class of some periodic orbit, and that there is an SRB-measure supported on the attractor.

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Mathematics Subject Classification: Primary: 37D10, 37D30.

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