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Recurrence in generalized semigroup

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  • Kushal Lalwani

    (University of Delhi)

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.

Suggested Citation

  • Kushal Lalwani, 2021. "Recurrence in generalized semigroup," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 216-223, March.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:1:d:10.1007_s13226-021-00076-x
    DOI: 10.1007/s13226-021-00076-x
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