Recurrence in generalized semigroup

Kushal Lalwani ()
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Kushal Lalwani: University of Delhi

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 216-223

Abstract: Abstract In [6], we introduced the concept of escaping set in general setting for a topological space and extended the notion of $$\omega $$ ω -limit set and escaping set for the general semigroup generated by continuous self maps. In this paper we continue with extending the other notions of recurrence for the generalized semigroup analogous to their counterpart in the classical theory of dynamics. We discuss the concept of periodic point, nonwandering point and chain recurrent point in the more general setting and establish the correlation between them. We shall also extend the Poincar $$\acute{e}$$ e ´ recurrence theorem in this setting.

Keywords: Chain recurrent set, Nonwandering set, Omega limit set; recurrence; 54H20; 37B20; 54H15 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00076-x

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