2019/07/15 by Nic Ormes, Ormes, Nic, Ronnie Pavlov +1
Computer Science · Materials Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1907.06626
openalex publication_date 2019/07/15 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We prove that every non-minimal transitive subshift X satisfying a mild\naperiodicity condition satisfies limsup cn(X) - 1.5n = \∞, and give a\nclass of examples which shows that the threshold of 1.5n cannot be increased.\nAs a corollary, we show that any transitive X satisfying limsup cn(X) - n\n= \∞ and limsup cn(X) - 1.5n < \∞ must be minimal. We also prove\nsome restrictions on the structure of transitive non-minimal X satisfying\n liminf cn(X) - 2n = -\∞, which imply unique ergodicity (for a periodic\nmeasure) as a corollary, which extends a result of Boshernitzan from the\nminimal case to the more general transitive case.\n