Sharkovskĭi Theorem for Multidimensional Perturbations of One-dimensional Maps Ii

@inproceedings{Zgliczynski1999SharkovskiTF,
  title={Sharkovskĭi Theorem for Multidimensional Perturbations of One-dimensional Maps Ii},
  author={Piotr Zgliczynski},
  year={1999}
}
We present a multidimensional generalization of the Sharkovskĭı Theorem concerning the appearance of periodic points for the self-maps on the real line. Introduction Let f : X → X be a map. We say that x ∈ X is a periodic point of period n if f(x) = x and f(x) 6= x for k = 1, . . . , n− 1. We begin with recalling the Sharkovskĭı Theorem. Theorem 1. Let the ordering of positive integers be as follows: 3 C 5 C 7 C . . . C 2 · 3 C 2 · 5 C 2 · 7 C . . . C 22 · 3 C 22 · 5 C . . . C 23 · 3 C 23 · 5 C… CONTINUE READING
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