Ergodic Shadowing of Semigroup Actions
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The present work is concerned with the ergodic shadowing property of semigroup actions. We prove that any finitely generated semigroup with the ergodic shadowing property has the ordinary shadowing property, and some properties for semigroup actions with the ergodic shadowing property such as topologically mixing, chain mixing, and weakly mixing are investigated. Finally, we define some kind of specification property and clarify its relation to the ergodic shadowing property.
KeywordsErgodic shadowing property Shadowing property Iterated function system Mixing
Mathematics Subject Classification35B41 37E30
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