# pseudo-orbit

Let $(X,d)$ be a metric space, $f\colon X\to X$ a function, and let $\epsilon>0$. An $\epsilon$-pseudo-orbit for $f$ is a sequence $\{x_{n}:n\in\mathbb{Z},\,a, where $-\infty\leq a, such that $d(x_{n+1},f(x_{n}))<\epsilon$ for all $a. A periodic pseudo-orbit is an infinite pseudo-orbit $\{x_{n}\}$ such that there is some $p$ with $x_{n+p}=x_{n}$ for all n.

Given $\delta>0$, the pseudo-orbit $\{x_{n}:a is said to be $\delta$-shadowed by the orbit of $x$, if $d(x_{n},f^{n}(x))<\delta$ for all $a.

Title pseudo-orbit Pseudoorbit 2013-03-22 14:07:19 2013-03-22 14:07:19 Koro (127) Koro (127) 7 Koro (127) Definition msc 37C50 pseudo orbit $\epsilon$-pseudo-orbit $\epsilon$-orbit $\epsilon$-chain shadow shadowing shadowed