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Recurrence in generalized semigroup

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Abstract

In [6], we introduced the concept of escaping set in general setting for a topological space and extended the notion of \(\omega \)-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\(\acute{e}\) recurrence theorem in this setting.

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Acknowledgements

I thank the referees for their helpful comments. Also I am thankful to my thesis adviser Sanjay Kumar for fruitful discussions.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110 007, India

    Kushal Lalwani

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  1. Kushal Lalwani
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Correspondence to Kushal Lalwani.

Additional information

Communicated by Kaushal Verma.

This work was supported by research fellowship from University Grants Commission (UGC), New Delhi.

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Lalwani, K. Recurrence in generalized semigroup. Indian J Pure Appl Math 52, 216–223 (2021). https://doi.org/10.1007/s13226-021-00076-x

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  • DOI: https://doi.org/10.1007/s13226-021-00076-x

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