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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Forthcoming papers   > Article

[Forthcoming] Attractors and chain recurrence for semigroup of continuous maps

[Forthcoming] Attracteurs et chaîne de récurrence pour le semi-groupe des fonctions continues


Kushal Lalwani
University of Delhi
India



Published on 13 January 2022   DOI :

Abstract

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In [12], we extended various notions of recurrence for the action of a semigroup analogous to their counterpart in the classical theory of dynamics. In this paper, we shall address the alternative de-nition of chain recurrent set in terms of attractors, given by Hurley in [10] following Conley’s characterization in [5]. We shall also discuss the notion of topological transitivity and chain transitivity in this general setting.

In [12], we extended various notions of recurrence for the action of a semigroup analogous to their counterpart in the classical theory of dynamics. In this paper, we shall address the alternative de-nition of chain recurrent set in terms of attractors, given by Hurley in [10] following Conley’s characterization in [5]. We shall also discuss the notion of topological transitivity and chain transitivity in this general setting.

attractor chain recurrent set omega limit set transitivity

attractor chain recurrent set omega limit set transitivity