Glider automata on all transitive sofic shifts

Normal amenable subgroups of the automorphism group of sofic shifts

Let $(X, σ)$ be a transitive sofic shift and let $\rm{Aut}(X)$ denote its automorphism group. We generalize a result of Frisch, Schlank, and Tamuz to show that any normal amenable subgroup of $\rm{Aut}(X)$ must be contained in the subgroup generated by the shift. We also show that the result does not extend to higher dimensions by giving an example of a two-dimensional mixing shift of finite type whose automorphism group is amenable and not generated by the shift maps.

($\times m, \times n$)-不变集的盒维数

Box dimensions of $(\times m, \times n)$-invariant sets

本文研究环面自同态不变集的盒维数，在非混合 sofic 情形下建立熵界，并给出编码子移位及非传递 sofic 情形的精确公式。

No Tits alternative for cellular automata

We show that the automorphism group of a one-dimensional full shift (the group of reversible cellular automata) does not satisfy the Tits alternative. That is, we construct a finitely-generated subgroup which is not virtually solvable yet does not contain a free group on two generators. We give constructions both in the two-sided case (spatially acting group $\Z$) and the one-sided case (spatially acting monoid $\N$, alphabet size at least eight). Lack of Tits alternative follows for several groups of symbolic (dynamical) origin: automorphism groups of two-sided one-dimensional uncountable sof…