2008/10/21 by Mario Bessa, Jorge Rocha, Bessa, Mario +1
Mathematics · #37A99 #37C10 (Secondary) #37D25 (Primary) #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37A99 #msc:37C10 #msc:37D25 #msc:37D30
paper · pdf · doi:10.48550/arxiv.0810.3855
26 pages, 2 figures
arxiv created 2008/10/21 · arxiv updated 2009/12/01
We prove the following dichotomy for vector fields in a C1-residual subset of volume-preserving flows: for Lebesgue almost every point all Lyapunov exponents equal to zero or its orbit has a dominated splitting. As a consequence if we have a vector field in this residual that cannot be C1-approximated by a vector field having elliptic periodic orbits, then, there exists a full measure set such that every orbit of this set admits a dominated splitting for the linear Poincare flow. Moreover, we prove that a volume-preserving and C1-stably ergodic flow can be C1-approximated by another volume-preserving flow which is non-uniformly hyperbolic.