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 $\\{x_{n}:n\\in\\mathbb{Z},\\,a<n<b\\}$ , where $-\\infty\\leq a<b\\leq\\infty$ , such that $d(x_{n+1},f(x_{n}))<\\epsilon$ for all $a<n<b$ . 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 $\\{x_{n}:a<n<b\\}$ is said to be $\\delta$ -shadowed by the orbit of $x$ , if $d(x_{n},f^{n}(x))<\\delta$ for all $a<n<b$ .

单词	Pseudoorbit
释义	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 $\\{x_{n}:n\\in\\mathbb{Z},\\,a<n<b\\}$ , where $-\\infty\\leq a<b\\leq\\infty$ , such that $d(x_{n+1},f(x_{n}))<\\epsilon$ for all $a<n<b$ . 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 $\\{x_{n}:a<n<b\\}$ is said to be $\\delta$ -shadowed by the orbit of $x$ , if $d(x_{n},f^{n}(x))<\\delta$ for all $a<n<b$ .
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