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- W2088448683 abstract "Let G be a graph and f:G→G be a continuous map. Denote by P(f), R(f) and Ω(f) the sets of periodic points, recurrent points and non-wandering points of f, respectively. In this paper we show that: (1) If L=(x,y) is an open arc contained in an edge of G such that {fm(x),fk(y)}⊂(x,y) for some m,k∈N, then R(f)∩(x,y)≠∅; (2) Any isolated point of P(f) is also an isolated point of Ω(f); (3) If x∈Ω(f)−Ω(fn) for some n∈N, then x is an eventually periodic point. These generalize the corresponding results in W. Huang and X. Ye (2001) [9] and J. Xiong (1983, 1986) [17], [19] on interval maps or tree maps." @default.
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- W2088448683 date "2011-11-01" @default.
- W2088448683 modified "2023-09-28" @default.
- W2088448683 title "Recurrent points and non-wandering points of graph maps" @default.
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- W2088448683 doi "https://doi.org/10.1016/j.jmaa.2011.05.052" @default.
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