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March  2007, 19(1): 67-87. doi: 10.3934/dcds.2007.19.67

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, Mexico
2. 

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

Received  August 2005 Revised  April 2007 Published  June 2007

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.
Keywords: Singular-Hyperbolicity, Attractors., 3-dimensional Flows.
Mathematics Subject Classification: Primary: 37D10, 37D3.
Citation: Aubin Arroyo, Enrique R. Pujals. Dynamical properties of singular-hyperbolic attractors. Discrete & Continuous Dynamical Systems, 2007, 19 (1) : 67-87. doi: 10.3934/dcds.2007.19.67
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