Global Orbit Patterns for Dynamical Systems On Finite Sets

Details Global Orbit Patterns for Dynamical Systems On Finite Sets Global Orbit Patterns for Dynamical Systems On Finite Sets

2009-03-22

arxiv.org/abs/0903.3728v1

Mathematics

Dynamical Systems

29 pages, 3 figures. to appear in Proceedings of the International Conference On Modeling of Engineering & Technological Probl

Scientific paper

In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set $X$ allows us to describe precisely the behaviour of such systems. We can predict by means of closed formulas, the number of gop of the set of all the function from $X$ to itself. We also explore, using the brute force of computers, some subsets of locally rigid functions on $X$, for which interesting patterns of periodic orbits are found.

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