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

Ultrafilter-limit points in metric dynamical systems

Salvador García-Ferreira, Manuel Sanchis (2007)

Commentationes Mathematicae Universitatis Carolinae

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Given a free ultrafilter p on ℕ and a space X , we say that x ∈ X is the p -limit point of a sequence ( x n ) n ∈ ℕ in X (in symbols, x = p - lim n → ∞ x n ) if for every neighborhood V of x , { n ∈ ℕ : x n ∈ V } ∈ 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 → X is defined by f p ( x ) = p - lim n → ∞ f n ( x ) for each x ∈ X . These functions are not continuous in general....