Sharkovskiǐ type of cycles

Academic Article

Abstract

  • The Sharkovskiǐ type of a map of an interval is the Sharkovskiǐ-greatest integer t such that it has a periodic point of period t. The Sharkovskǐ type of a cycle (that is, a cyclic permutation) is the Sharkovskiǐ type of the 'connect the dots' map determined by it. For n ≥ 2, let ℓ (n) denote the finite set of integers which are Sharkovskiǐ types of n-cycles. We give an internal characterization of ℓ(n) and an n4-time algorithm for determining the Sharkovskiǐ type of an n-cycle.
  • Digital Object Identifier (doi)

    Author List

  • Blokh AM; Coven EM
  • Start Page

  • 417
  • End Page

  • 424
  • Volume

  • 28
  • Issue

  • 4