We direct the reader to for a discussion of such systems. Some reasons that these subshifts are of great in-terest are that every subshift contains a minimal subshift, and many naturalexamples of subshifts, such as those generated by primitive substitutions andthose generated by Toeplitz sequences, are minimal. These are precisely the nonempty subshifts containing no propernonempty (sub-)subshifts. One of the most studied classes of subshifts in the literature is that of mini-mal subshifts. With N -actions, their theory essentially reduces to thetheory of minimal systems, but with Z -actions, the class is much larger.We show many examples of such subshifts, and in particular construct auniversal system with only a single proper subsystem, refuting a conjec-ture of. We introduce the quasiminimal subshifts, subshifts having only finitelymany subsystems. J a n Decidability and Universality of QuasiminimalSubshifts Chang, Characterization for entropy of shifts of finite type on Cayley trees, J. Li, Entropy and the variational principle foractions of sofic groups, Invent. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Coornaert, Cellular Automata and Groups, Springer-Verlag Berlin Heidelberg, 2010.ĭ. Bowen, Measure conjugacy invariants for actions of countable sofic groups, J. Thouvenot, Slow entropy type invariants and smooth realization of commutingmeasure-preserving transformations, Ann. Urbański, Measure-theoretic degrees and topological pressure for nonexpanding transformations, J. Park, Entropy dimension of measure preserving systems, 2018, arXiv:1312.7225.Į. Park, Entropy dimension of topological dynamical systems, Trans. Carvalho, Entropy dimension of dynamical systems, Port. Pietrzyk, Quasi-uniformconvergenceindynamical systems generated by an amenable group action, 2016, arXiv:1610.09675. Jeandel, Aperiodic subshifts of finite type on groups, 2015. Tamuz, Symbolic dynamics on amenable groups: The entropy of generic shifts, 2015. Cohen, The large scale geometry of strongly aperiodic subshifts of finite type, Adv. Stein, The domino problem on groups of polynomial growth, 2013. Marcus, Mixing properties for hom-shifts and the distance between walks on associated graphs, Pacific J. Salama, Tree shift topological entropy, Theoret.
Toeplitz subshift conjugacy invariant free#
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