Parameter-shifted shadowing property of Lozi maps

Abstract

In this article, we study a certain shadowing property on well-known two-dimensional maps presented by Lozi with the y-axis as their singularity set and strange attractors. Our main theorem shows that there exists a nonempty open subset of the Misiurewicz domain such that, for any , the Lozi map L a , b with strange attractor has the parameter-shifted shadowing property.