Let (X,d) be a metric space, f:XX a function, and let ϵ>0. An ϵ-pseudo-orbit for f is a sequence {xn:n,a<n<b}, where -a<b, such that d(xn+1,f(xn))<ϵ for all a<n<b. A periodic pseudo-orbit is an infinite pseudo-orbit {xn} such that there is some p with xn+p=xn for all n.

Given δ>0, the pseudo-orbit {xn:a<n<b} is said to be δ-shadowed by the orbit of x, if d(xn,fn(x))<δ for all a<n<b.

Title pseudo-orbit
Canonical name Pseudoorbit
Date of creation 2013-03-22 14:07:19
Last modified on 2013-03-22 14:07:19
Owner Koro (127)
Last modified by Koro (127)
Numerical id 7
Author Koro (127)
Entry type Definition
Classification msc 37C50
Synonym pseudo orbit
Synonym ϵ-pseudo-orbit
Synonym ϵ-orbit
Synonym ϵ-chain
Defines shadow
Defines shadowing
Defines shadowed