Induced dynamics on the hyperspaces

• Autores: Puneet Sharma
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 17, Nº. 2, 2016, págs. 93-104
• Idioma: inglés
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• Resumen

  •  In this paper, we study the dynamics induced by finite commutative relation on the hyperspaces. We prove that the dynamics induced on the hyperspace by a non-trivial commutative family of continuous self maps cannot be transitive and hence cannot exhibit higher degrees of mixing. We also prove that the dynamics induced on the hyperspace by such a collection cannot have dense set of periodic points. We also give example to show that the induced dynamics in this case may or may not be sensitive.