Topological stability of semigroup actions and shadowing

2025/02/11 by Ceccherini-Silberstein, Tullio, Coornaert, Michel, Phung, Xuan Kien · 2 citations
#20M30 #37B05 #37B10 #37B51 #37B65 #37C20 #37D20 #54H15 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2502.07984

Abstract

We investigate expansiveness, topological stability, and shadowing for continuous actions of semigroups on compact Hausdorff spaces. We characterize semigroups for which all full shifts are expansive. We show that every expansive continuous monoid action on a compact Hausdorff space which has the shadowing property is topologically stable, and that a subshift with finite alphabet over a monoid has the shadowing property if and only if it is of finite type.

Cited by

• Expansivity of algebraic semigroup actions
• Topological Stability and Shadowing in Uniform Transformation Semigroups Modulo an Ideal

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