Classification of the Second Minimal Odd Periodic Orbits in the Sharkovskii Ordering

Ugur G. Abdulla; Rashad U. Abdulla; Muhammad U. Abdulla; Naveed H. Iqbal

paper

Classification of the Second Minimal Odd Periodic Orbits in the Sharkovskii Ordering

arXiv:1701.02695

Abstract

This paper presents full classification of second minimal odd periodic orbits of a continuous endomorphisms on the real line. A $(2 k + 1)$ -periodic orbit ( $k \geq 3$ ) is called second minimal for the map $f$ , if $2 k - 1$ is a minimal period of $f$ in the Sharkovskii ordering. We prove that there are $4 k - 3$ types of second minimal $(2 k + 1)$ -orbits, each characterized with unique cyclic permutation and directed graph of transitions with accuracy up to inverses.

32 pages, 39 figures, 2 tables