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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.24 n.1 Antofagasta mayo 2005

http://dx.doi.org/10.4067/S0716-09172005000100003 

 

Proyecciones
Vol. 24, No 1, pp. 21-35, May 2005.
Universidad Católica del Norte
Antofagasta - Chile

REVERSIBILITY FOR SEMIGROUP ACTIONS*

LUIZ A. B. SAN MARTIN †
Universidade Estadual de Campinas, Brasil.

OSVALDO G. DO ROCIO
Universidade Estadual de Maringá, Brasil.

and

ALEXANDRE J. SANTANA
Universidade Estadual de Maringá, Brasil.

Correspondencia a :


ABSTRACT

Let Q be a topological space and S a semigroup of local homeomorphisms of Q. The purpose of this paper is to generalize the notion of reversibility and to introduce the reversible sets. And furthermore, it is established a relation between these sets and the control sets for S and it is studied reversibility of semigroup actions on fiber bundles.

Key words: Semigroups, reversibility, fiber bundles, control sets.

AMS 2000 subject classification: 20M20, 22E46, 57S25.


References

[1] Arnold,L.; Kliemann, K. and Oeljeklaus, E.: Lyapunov exponents of linear stochastic systems. In Lyapunov Exponents (Arnold,L. andWihstutz, V. eds.) LNM-Springer Vol. 1186, (1986).        [ Links ]

[2] Braga Barros, C.J.; San Martin, L.A.B.: On the action of semigroups in fiber bundles. Mat. Comtemp., SBM, Vol. 15, 3, pp. 257-276, (1996).        [ Links ]

[3] Colonius, F. ; Kliemann, W: Dynamics and control. Birkhäuser,(2000).        [ Links ]

[4] Furstenberg, H., A Poisson formula for semi-simple Lie groups. Ann. of Math. 77, pp. 335-386, (1963).        [ Links ]

[5] Hilgert, J. ; Neeb, K.-H.: Lie semigroups and their applications. Lecture Notes in Math. 1552. (Springer, Berlin 1993).        [ Links ]

[6] Kobayashi, S.; Nomizu, K.: Foundations of dierential geometry. John Willey & Sons, (1963).        [ Links ]

[7] Rocio, O.G. ; San Martin, L. A. B.: Connected components of open semi groups in semi-simples Lie groups. To appear in Semigroup Forun.        [ Links ]

[8] Ruppert, W.A.F.: On open subsemigroups of connected groups. Semigroup Forum Vol. 50, pp. 59-88, (1995).        [ Links ]

[9] San Martin, L.A.B.: Invariant control sets on flag manifolds. Math. Control Signals Systems 6, pp. 41-61, (1993).         [ Links ]

[10] SanMartin, L.A.B.: Semigroups of local homeomorphisms. Submitted.        [ Links ]

[11] San Martin, L.A.B. ; Santana, A.J.: The homotopy type of Lie semigroups in semi-simple Lie groups. Monatsh. Math. 136, pp. 151-173,(2002).        [ Links ]

[12] San Martin, L.A.B. ; Tonelli, P.A.: Semigroup actions on homogeneous spaces. Semigroup Forum 50, pp. 59-88, (1995).        [ Links ]

Received : December 2004. Accepted : April 2005.

*Research partially supported by CAPES/PROCAD, grant N 00186/00-7

†Supported by CNPq N 301060/94-0.

Luiz A. B. San Martin
Departamento de Matemática
Universidade Estadual de Campinas
Caixa Postal: 6065
13083-859 Campinas SP
Brasil
smartin@ime.unicamp.br

Osvaldo Germano do Rocio
Departamento de Matemática
Universidade Estadual de Maringá
87020-900 Maringá Pr
Brasil
rocio@uem.br

and

Alexandre J. Santana
Departamento de Matemática
Universidade Estadual de Maringá
87020-900 Maringá Pr
Brasil
ajsantana@uem.br