Periods of orbits for maps on graphs homotopic to a constant map

2011/08/14 by Chris Bernhardt, Bernhardt, Chris, Zach Gaslowitz +5
Mathematics · #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals #math.DS #msc:37E15 #msc:37E25 #msc:37E45

paper · pdf · doi:10.48550/arxiv.1108.2899

15 pages, 1 figure

arxiv created 2012/04/25 · arxiv updated 2012/04/26

Abstract

The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if v is not a divisor of 2^k then there must be a periodic point with period 2^k. The second is that if v=2^ks for odd s>1, then for all r>s there exists a periodic point of minimum period 2^k r. These results are then compared to the Sharkovsky ordering of the positive integers. (The final version of this paper will appear in the Journal of Difference Equations and Applications.)

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