Beyond topological hyperbolicity: The L-shadowing property

On the Notion of Fuzzy Shadowing Property

This paper is concerned with the study of fuzzy dynamical systems. Let (XM ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map dened on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.

On Periodic Shadowing Property

In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...

Semi-Hyperbolicity and Bi-Shadowing

Preface In the beginning of 90s the authors of this monograph proposed a generalization of the concept of hyperbolicity, first for differentiable mappings and later for Lipschitz mappings, which they called 'semi-hyperbolicity'. This arose indirectly in the context of their research at that time on the effect of spatial discretization on the behavior of a dynamical system, in particular that of...

Continuous Inverse Shadowing and Hyperbolicity

We study the concepts of continuous shadowing and continuous inverse shadowing with respect to various classes of admissible pseudo orbits, and characterize hyperbolicity and structural stability using the notion of continuous inverse shadowing.

Beyond Hyperbolicity