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Qualitative Theory of Dynamical Systems

, Volume 15, Issue 1, pp 181–210 | Cite as

Simple Permutations with Order \(4n+2\) by Means of Pasting and Reversing

  • Primitivo B. Acosta-HumánezEmail author
  • Óscar E. Martínez-Castiblanco
Article
  • 54 Downloads

Abstract

The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Humánez and Bernhardt (power of two). It is well known that Sharkovskii’s theorem shows the relationship between the cardinal of the set of periodic points of a continuous map, but simple permutations will show the behaviour of those periodic points. Recently Abdulla et al studied the structure of minimal \(4n+2\)-orbits of the continuous endomorphisms on the real line. This paper studies some combinatorial dynamics structures of permutations of mixed order \(4n+2\), describing its genealogy, using Pasting and Reversing.

Keywords

Block’s orbits Combinatorial dynamics Markov graphs Pasting Periodic points Reversing Sharkovskii’s Theorem Simple permutations 

Mathematics Subject Classification

Primary 37E15 Secondary 05A05 37A99 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Primitivo B. Acosta-Humánez
    • 1
    • 2
    Email author
  • Óscar E. Martínez-Castiblanco
    • 3
  1. 1.Department of MathematicsUniversidad del AtlánticoKM 7 via Puerto ColombiaColombia
  2. 2.INTELECTUAL.COPradomarPuerto Colombia
  3. 3.School of MathematicsUniversidad Sergio ArboledaBogotáColombia

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