Weak Strictly Persistence Homeomorphisms and Weak Inverse shadowing and Genericity-

نویسنده:
, , ,
سال
: 2009
چکیده: In this paper we introduce the notions of strict persistence and weakly strict

persistence which are stronger than those of persistence and weak persistence, respectively,

and study their relations with shadowing property. In particular, we show that the weakly

strict persistence and the weak inverse shadowing property are locally generic in Z(M).

1. Introduction

Let (M; d) be a compact metric space and let f : M ! M be a homeomorphism

(a discrete dynamical system on M). A sequence fxngn2Z is called an orbit of f,

denote by o(x; f), if for each n 2 Z, xn+1 = f(xn) and is called a -pseudo-orbit of

f if

d(f(xn); xn+1) ; 8n 2 Z:

We denote the set of all homeomorphisms of M by Z(M). Introduce in Z(M) the

complete metric

d0(f; g) = maxfmaxx2Md(f(x); g(x)); maxx2Md(f
کلیدواژه(گان): inverse shadowing property,persistence -pseudo-orbit,shadowing

property
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