2003/03/25 by C. A. Morales, Morales, C. A., M. J. Pacifico +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37D30 #Secondary 37D50 #math.DS #msc:37D30 #msc:37D50
paper · pdf · doi:10.48550/arxiv.math/0303309
19 pages, 6 figures
arxiv created 2003/03/25 · arxiv updated 2009/11/30
A \em singular hyperbolic set is a partially hyperbolic set with singularities (all hyperbolic) and volume expanding central direction \citeMPP1. We study connected, singular-hyperbolic, attracting sets with dense closed orbits \em and only one singularity. These sets are shown to be transitive for most Cr flows in the Baire's second category sence. In general these sets are shown to be either transitive or the union of two homoclinic classes. In the later case we prove the existence of finitely many homoclinic classes. Our results generalize for singular-hyperbolic systems a well known result for hyperbolic systems in \citeN.