Center Fitting Shadowing Property for Partial Hyperbolic Diffeomorphisms

Abstract

The idea of shadowing in dynamical systems theory (DS) is to approximate the pseudo-orbit (PO) of certain dynamical systems (DS) by real orbits of course, depending on the type of approximation. The aim of this work to explain the stable fitting shadowing property for partially hyperbolic diffeomorphism, to clarification that if partially hyperbolic diffeomorphism contain $w_{i}$, where $i=1,2$ saddle points with indices not equal, then $\mathcal{L}:M\rightarrow M$ does not satisfy the fitting shadowing property FSP. On other hand can be achieved fitting shadowing property of a closed $C^{\infty}$ of M(i.e., boundary less and compact) if the center is uniformly compact center foliation $(W^{c})$, to proof the main Theorem K.