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- W2167662605 abstract "Let G be a graph and f:G→G be continuous. Denote by P(f), P(f)¯, ω(f) and Ω(f) the set of periodic points, the closure of the set of periodic points, ω-limit set and non-wandering set of f, respectively. In this paper we show that: (1) v∈ω(f) if and only if v∈P(f) or there exists an open arc L=(v,w) contained in some edge of G such that every open arc U=(v,c)⊂L contains at least 2 points of some trajectory; (2) v∈ω(f) if and only if every open neighborhood of v contains at least r+1 points of some trajectory, where r is the valence of v; (3) ω(f)=⋂n=0∞fn(Ω(f)); (4) if x∈ω(f)−P(f)¯, then x has an infinite orbit." @default.
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- W2167662605 date "2007-06-01" @default.
- W2167662605 modified "2023-09-28" @default.
- W2167662605 title "The ω-limit set of a graph map" @default.
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- W2167662605 doi "https://doi.org/10.1016/j.topol.2007.03.008" @default.
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