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).
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