On the determination of the potential function from given orbits

L. Alboul; J. Mencía; R. Ramírez; N. Sadovskaia

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Displaying similar documents to “On the determination of the potential function from given orbits”

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Given a free ultrafilter $p$ on $ℕ$ and a space $X$ , we say that $x \in X$ is the $p$ -limit point of a sequence ${(x_{n})}_{n \in ℕ}$ in $X$ (in symbols, $x = p$ - ${lim}_{n \to \infty} x_{n}$ ) if for every neighborhood $V$ of $x$ , ${n \in ℕ : x_{n} \in V} \in p$ . By using $p$ -limit points from a suitable metric space, we characterize the selective ultrafilters on $ℕ$ and the $P$ -points of $ℕ^{*} = β (ℕ) ∖ ℕ$ . In this paper, we only consider dynamical systems $(X, f)$ , where $X$ is a compact metric space. For a free ultrafilter $p$ on $ℕ^{*}$ , the function $f^{p} : X \to X$ is defined by $f^{p} (x) = p$ - ${lim}_{n \to \infty} f^{n} (x)$ for each $x \in X$ . These functions are not continuous in general....

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