Vector Fields with the Asymptotic Orbital Pseudo-orbit Tracing Property.

In this paper, we introduce the notion of the asymptotic orbital pseudo-orbit tracing property for a vector field X of a compact smooth manifold M. We show that if a vector field X has the C 1 robust asymptotic orbital pseudo-orbit tracing property, then it is Anosov, and if a C 1 generic vector field X has the asymptotic orbital pseudo-orbit tracing property, then it is Anosov. Moreover, we also show our results for divergence-free vector fields and Hamiltonian systems. [ABSTRACT FROM AUTHOR]