Asymptotic behavior of dynamical systems and cellular automata

Details Asymptotic behavior of dynamical systems and cellular automata Asymptotic behavior of dynamical systems and cellular automata

2010-04-27

arxiv.org/abs/1004.4743v3

Mathematics

Dynamical Systems

28p

Scientific paper

We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we deal with the case when each of these are a singleton, or when the restriction of the system is periodic on them, and show that this is equivalent to some simple dynamics in the case of subshifts or cellular automata. Moreover, we deal with the stability of these properties with respect to some simulation notions.

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