Proyecciones Journal of Mathematics
Vol. 30, N° 1, pp. 65-75, May 2011.
Universidad Católica del Norte
Antofagasta - Chile


Examples of Morse decompositions for semigroups actions


Carlos J. Braga Barros
Hélio V. M. Tozatti
Josiney A. Souza†

Universidade Estadual de Maringá, Brasil


Correspondencia a:

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Abstract

The concepts of Morse decompositions and dynamic Morse decompositions are equivalent for flows. In this paper we show that these concepts are not equivalent for Morse decompositions of semigroup of homeomorphisms on topological spaces. We give an example of a dynamic Morse decomposition which is not a Morse decomposition on compactifications of topological spaces. Other examples of Morse decompositions are also provided.

Mathematics Subject Classification (2000) : 37B35. 37B25.

Keywords : Morse decomposition, dynamic Morse decomposition, one-point compactification.

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References

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Carlos J. Braga Barros
Departamento de Matemática
Universidade Estadual de Maringá
Maringá-PR Brasil 87020-900
e-mail : cjbbarros@uem.br


Hélio V. M. Tozatti
Departamento de Matemática
Universidade Estadual de Maringá
Maringá-PR Brasil 87020-900
e-mail : hvlomuert@hotmail.com


Josiney A. Souza
Departamento de Matemática
Universidade Estadual de Maringá
Maringá-PR Brasil 87020-900
e-mail : jasouza3@uem.br

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Received : December 2010. Accepted : March 2011