QUASI-SHADOWING FOR PARTIALLY HYPERBOLIC FLOWS

In this paper, we study the quasi-shadowing property for partially hyperbolic flows. A partially hyperbolic flow phi(t) has the quasi-shadowing property if for any (delta, T)-pseudoorbit g(t) of phi(t) there exist a sequence of points {yk}k is an element of Z and a reparametrization alpha such that phi(alpha(t)-alpha(kT)) (yk) trace g(t) in which yk is obtained from phi(alpha(kT)-alpha ((k-1)T)) (Yk-1) by a motion along the central direction. We prove that any partially hyperbolic flow phi(t) has the quasi-shadowing property. We also investigate the limit quasi-shadowing properties for flows. That is, a partially hyperbolic flow has the L-p, limit and asymptotic quasi-shadowing properties.