On the predictability of discrete dynamical systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the predictability of discrete dynamical systems

Authors:	Nilson C Bernardes Jr

Institution:	Instituto de Matemática, Universidade Federal Fluminense, Rua Mário Santos Braga s/n, 24020-140, Niterói, RJ, Brasil

Abstract:	Let be a metric space. A function $f: X \to X$ is said to be non-sensitive at a point $a \in X$ if for every $\epsilon > 0$ there is a $\delta > 0$ such that for any choice of points $a_0 \in B(a;\delta)$ , $a_1 \in B(f(a_0);\delta)$ , $a_2 \in B(f(a_1);\delta),\ldots$ , we have that $d(a_m,f^m(a)) < \epsilon$ for every $m \geq 0$ . Let be the set of all homeomorphisms from onto endowed with the topology of uniform convergence. The main goal of the present paper is to prove that for certain spaces , ``most' functions in are non-sensitive at ``most' points of .

Keywords:	Homeomorphisms predictability recurrence Baire category Lebesgue measure

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