Author:
Pavlov Ronnie,Schmieding Scott
Abstract
Abstract
We investigate generic properties (i.e. properties corresponding to residual sets) in the space of subshifts with the Hausdorff metric. Our results deal with four spaces: the space S of all subshifts, the space
S
′
of non-isolated subshifts, the closure
T
′
‾
of the infinite transitive subshifts, and the closure
T
T
′
‾
of the infinite totally transitive subshifts. In the first two settings, we prove that generic subshifts are fairly degenerate; for instance, all points in a generic subshift are biasymptotic to periodic orbits. In contrast, generic subshifts in the latter two spaces possess more interesting dynamical behavior. Notably, generic subshifts in both
T
′
‾
and
T
T
′
‾
are zero entropy, minimal, uniquely ergodic, and have word complexity which realizes any possible subexponential growth rate along a subsequence. In addition, a generic subshift in
T
′
‾
is a regular Toeplitz subshift which is strongly orbit equivalent to the universal odometer.
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献