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arXiv · 1701.02695

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

Ugur G. Abdulla·Rashad U. Abdulla·Muhammad U. Abdulla·Naveed H. Iqbal
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Abstract

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

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Ugur G. Abdulla, Rashad U. Abdulla, Muhammad U. Abdulla, Naveed H. Iqbal. 2017-01-10. Classification of the Second Minimal Odd Periodic Orbits in the Sharkovskii Ordering. https://arxiv.org/abs/1701.02695

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