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1 results

  • Non-wandering points and the depth of a graph map

  • Part of
  • Xiangdong Ye
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 69 / Issue 2 / October 2000
    Published online by Cambridge University Press:
    09 April 2009, pp. 143-152
    Print publication:
    October 2000
    • Article
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  • Lef: G → G be a continuous map of a graph and let d(A) denote the derived set (or limit points) of A ⊂ G. We prove that d(Ω(f)) ⊂ λ (f) and the depth of f is at most three. We also prove that if f is piecewise monotone or has zero topological entropy, then the depth of f is at most two. Furthermore, we obtain some results on the topological structure of Ω(f).