English

A Simple Proof of Sharkovsky's Theorem Rerevisited

Dynamical Systems 2015-04-13 v9

Abstract

Based on various strategies and a new general doubling operator, we obtain several simple proofs of the celebrated Sharkovsky's cycle coexistence theorem. A simple non-directed graph proof which is especially suitable for a calculus course right after the introduction of Intermediate Value Theorem is also given (in section 3).

Keywords

Cite

@article{arxiv.0711.3892,
  title  = {A Simple Proof of Sharkovsky's Theorem Rerevisited},
  author = {Bau-Sen Du},
  journal= {arXiv preprint arXiv:0711.3892},
  year   = {2015}
}

Comments

28 pages, 5 figures, In this revision, we replace a detailed proof of (a), (b) and (c) in section 3 and a detailed proof of Sharkovsky's theorem in section 11. arXiv admin note: substantial text overlap with arXiv:math/0703592

R2 v1 2026-06-21T09:47:00.553Z