Examples of Morse decompositions for semigroups actions

Authors

  • Carlos J. Braga Barros Universidade Estadual de Maringá.
  • Hélio V. M. Tozatti Universidade Estadual de Maringá.
  • Josiney A. Souza Universidade Estadual de Maringá.

DOI:

https://doi.org/10.4067/S0716-09172011000100007

Keywords:

Morse decomposition, Dynamic Morse decomposition, one-point compactification.

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 semigroups of homeomorphisms on topological spaces.We give an example of a dynamic Morse decompositions on compactifications of topological spaces. Other examples of Morse decompositions are also provided. 

Author Biographies

Carlos J. Braga Barros, Universidade Estadual de Maringá.

Departamento de Matemática.

Hélio V. M. Tozatti, Universidade Estadual de Maringá.

Departamento de Matemática.

Josiney A. Souza, Universidade Estadual de Maringá.

Departamento de Matemática.

References

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[2] Braga Barros, C. J. and Souza, J. A. : Finest Morse decompositions for semigroup actions on Fiber Bundles. J. of Dyn. Diff. Eq. 22, pp. 741-750 (2010).

[3] Braga Barros, C. J., Souza, J. A. and Reis, R. A. : Dynamic Morse decompositions for semigroup of homeomorphisms and control systems. To appear (2011).

[4] Braga Barros, C. J. and San Martin, L. A. B. : Chain transitive sets for flows on flag bundles. Forum Math. 19, pp. 19-60, (2007).

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[7] Ellis, D. B., Ellis, R. and Nerurkar, M. : The topological dynamics of semigroup actions. Trans. Amer. Math. Soc. 353, pp. 1279-1320, (2000).

[8] Hirsch, W. M., Smith H. L. and Zhao, X. : Chain transitivity, attractivity and strong repellers for semidynamical systems. J. of Dyn. Diff. Eq. 13, pp. 107-131, (2001).

[9] Patrao, M. : Morse decomposition of semiflows on topological spaces. J. of Dyn. Diff. Eq. 19, pp. 181-198, (2007).

[10] Patrao, M. and San Martin, L. A. B. : Semiflows on topological spaces: chain transitivity and semigroups. J. of Dyn. Diff. Eq. 19, pp. 155-180, (2007).

[11] Patrao, M. and San Martin, L. A. B. : Morse decomposition of semi- flows on fiber bundles. Discrete and Continuous Dynamical Systems (Series A) 17, pp. 113-139 (2007).

Published

2011-05-25

How to Cite

[1]
C. J. Braga Barros, H. V. M. Tozatti, and J. A. Souza, “Examples of Morse decompositions for semigroups actions”, Proyecciones (Antofagasta, On line), vol. 30, no. 1, pp. 65-75, May 2011.

Issue

Section

Artículos