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

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

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

Dynamical Systems 2017-11-21 v2

Authors: Ugur G. Abdulla , Rashad U. Abdulla , Muhammad U. Abdulla , Naveed H. Iqbal

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.

Keywords

Sharkovskii ordering odd periodic orbits second minimal orbits continuous endomorphisms cyclic permutation directed graph of transitions classification

Cite

@article{arxiv.1701.02695,
  title  = {Classification of the Second Minimal Odd Periodic Orbits in the Sharkovskii Ordering},
  author = {Ugur G. Abdulla and Rashad U. Abdulla and Muhammad U. Abdulla and Naveed H. Iqbal},
  journal= {arXiv preprint arXiv:1701.02695},
  year   = {2017}
}

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32 pages, 39 figures, 2 tables

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

Abstract

Keywords

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