Quasi-Shadowing for Partially Hyperbolic Flows with a Local Product Structure

Let a flow phi(t) be partially hyperbolic on Lambda. If Lambda has a local product structure, then q t has the quasi-shadowing property on A in the following sense: for any epsilon > 0, there exists constant delta > 0 such that for any (delta, 1)-pseudo orbit {x(k), t(k)}(k is an element of Z) of phi(t) with 1 <= t(k) <= 2 for all k is an element of Z, there exist a sequence of points {y(k)}(k is an element of Z) and a reparametrization alpha is an element of Rep(R, epsilon) such that phi(alpha(t)-alpha)(Sigma(k))(y(k)) trace phi(t)-Sigma(k)(xk) in which y(k+1 )lies in the local center leaf of phi(alpha)(Sigma(k+1)) - alpha (Sigma(k)) (y(k)) for k >= 0 t >= 0 and phi(alpha(t)-alpha(-Sigma k))(y(k)) trace phi(t) -(-Sigma(k))(x(k)) in which y(k+1) lies in the local center leaf of phi(alpha)(-Sigma(k+1))-alpha(-Sigma(k))(y(k)) for k < 0, t < 0.