Partial hyperbolicity and central shadowing
  We study shadowing property for a partially hyperbolic diffeomorphism $f$. It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotrajectory with "jumps" along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem. 
Sergey Kryzhevich, Sergey Tikhomirov
math.DS