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

2017/01/10 by Ugur G. Abdulla, Rashad U. Abdulla, Abdulla, Ugur G. +6
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #05C20 #37D45 #37M20 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #Geomagnetism and Paleomagnetism Studies #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:05C20 #msc:37D45 #msc:37M20 #msc:54H20

paper · pdf · doi:10.48550/arxiv.1701.02695

32 pages, 39 figures, 2 tables

openalex publication_date 2017/01/10 · arxiv created 2017/11/19 · arxiv updated 2017/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥ 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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