2018/05/22 by Anael Grandjean, Grandjean, Anael, Benjamin Hellouin de Menibus +3 · 1 citation
Computer Science · Mathematics · #37B50 #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #G.2 #acm:37B50 #cs.DM #math.DS #msc:37B50
paper · pdf · doi:10.48550/arxiv.1805.08829
13 pages, accepted to ICALP 2018
arxiv created 2018/05/22 · arxiv updated 2018/05/24
We consider the structure of aperiodic points in \mathbb Z2-subshifts, and in particular the positions at which they fail to be periodic. We prove that if a \mathbb Z2-subshift contains points whose smallest period is arbitrarily large, then it contains an aperiodic point. This lets us characterise the computational difficulty of deciding if an \mathbb Z2-subshift of finite type contains an aperiodic point. Another consequence is that \mathbb Z2-subshifts with no aperiodic point have a very strong dynamical structure and are almost topologically conjugate to some \mathbb Z-subshift. Finally, we use this result to characterize sets of possible slopes of periodicity for \mathbb Z3-subshifts of finite type.