Weak Strictly Persistence Homeomorphisms and Weak Inverse shadowing and Genericity-

Abstract

In this paper we introduce the notions of strict persistence and weakly strict<br><br>persistence which are stronger than those of persistence and weak persistence, respectively,<br><br>and study their relations with shadowing property. In particular, we show that the weakly<br><br>strict persistence and the weak inverse shadowing property are locally generic in Z(M).<br><br>1. Introduction<br><br>Let (M; d) be a compact metric space and let f : M ! M be a homeomorphism<br><br>(a discrete dynamical system on M). A sequence fxngn2Z is called an orbit of f,<br><br>denote by o(x; f), if for each n 2 Z, xn+1 = f(xn) and is called a -pseudo-orbit of<br><br>f if<br><br>d(f(xn); xn+1) ; 8n 2 Z:<br><br>We denote the set of all homeomorphisms of M by Z(M). Introduce in Z(M) the<br><br>complete metric<br><br>d0(f; g) = maxfmaxx2Md(f(x); g(x)); maxx2Md(f