2015/05/25 by Primitivo B. Acosta-Humánez, Acosta-Humánez, Primitivo B., Oscar E. Martínez-Castiblanco +1
Mathematics · #37A99 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37E15 #Secondary 05A05 #math.DS #msc:05A05 #msc:37A99 #msc:37E15
paper · pdf · doi:10.48550/arxiv.1505.06581
29 pages, 4 figures
arxiv created 2015/05/25 · arxiv updated 2016/08/08
The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Humánez & 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.