A Simple Proof of Sharkovsky's Theorem Rerevisited

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).

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

References in corpus (1)

• A collection of simple proofs of Sharkovsky's theorem

Cited by in corpus (1)

• An Interesting Application of the Intermediate Value Theorem: A Simple Proof of Sharkovsky's Theorem and the Towers of Periodic Points