ABSTRACT: The language stable subshifts form a class of subshifts recently introduced by V. Cyr and B. Kra. This family contains many classical examples of subshifts, of various complexities: from positive entropy systems, such as subshifts of finite type, to low complexity systems, such as linear complexity subshifts. They are generic among the family of subshifts. In a joint work with V. Cyr and B. Kra we study some of their dynamical properties and rigidities.
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