Orbit shifted shadowing property of generalized Lozi maps (Q532973)

This paper studies some shadowing property of certain piecewise hyperbolic maps introduced by Young, which are generalized from a two-parameter family of planar maps presented by Lozi. The author investigates a certain shadowing property in which he shifts some entries of pseudo-orbits by rule instead of shifting parameters of maps, called the orbit-shifted shadowing property; and showed that certain piecewise Lozi-like maps enjoy this property. The proofs are not difficult but still rigorous. The results are only restricted to one class of systems and should be extended to a general class of hyperbolic systems with strong statistical properties.