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On limit behavior of semigroup actions on noncompact spaces

Author: Josiney A. Souza
Journal: Proc. Amer. Math. Soc. 140 (2012), 3959-3972
MSC (2010): Primary 37B35, 37B25
Published electronically: March 23, 2012
MathSciNet review: 2944735
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Abstract: This paper is produced in response to the questioning of Morse decomposition for semigroup actions on noncompact spaces. We show how the limit behavior can be studied in arbitrary topological spaces by using powerful tools such as the Stone-Čech compactification and shadowing semigroups. We extend Conley's characterization of chain recurrence in terms of attractors from the setting of flows on compact metric spaces to the setting of semigroup actions on any topological space.

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Josiney A. Souza
Affiliation: Departamento de Matemática, Universidade Estadual de Maringá, Maringá 87020-900, Brasil

Keywords: Semigroup actions, chain recurrence, Morse decompositions.
Received by editor(s): February 10, 2011
Received by editor(s) in revised form: May 12, 2011
Published electronically: March 23, 2012
Communicated by: Yingfei Yi
Article copyright: © Copyright 2012 American Mathematical Society