Dynamical properties of singular-hyperbolic attractors
Aubin Arroyo - UNAM - Instituto de Matemáticas, U. Cuernavaca, A.P. 273 Admon. de correos # 3, Cuernavaca, Morelos 62251, México, Mexico (email)
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.
Keywords: Singular-Hyperbolicity, 3-dimensional Flows, Attractors.
Received: August 2005; Revised: April 2007; Available Online: June 2007.
2014 IF (1 year).972