Reversibility For Semigroup Actions

• San Martin, Luiz A. B. ; Rocío, Osvaldo Germano do ; Santana, Alexandre J. ^[1]
  1. [1] Universidade Estadual de Maringá

     Universidade Estadual de Maringá

     Brasil

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 24, Nº. 1, 2005, págs. 21-35
• Idioma: inglés
• DOI: 10.4067/S0716-09172005000100003
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • Citas [1] Arnold, L.; Kliemann, K. and Oeljeklaus, E.: Lyapunov exponents of linear stochastic systems. In Lyapunov Exponents (Arnold,L....
  • [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).
  • [3] Colonius, F. ; Kliemann, W: Dynamics and control. Birkhäuser, (2000).
  • [4] Furstenberg, H., A Poisson formula for semi-simple Lie groups. Ann. of Math. 77, pp. 335-386, (1963).
  • [5] Hilgert, J. ; Neeb, K.-H.: Lie semigroups and their applications. Lecture Notes in Math. 1552. (Springer, Berlin 1993).
  • [6] Kobayashi, S.; Nomizu, K.: Foundations of differential geometry. John Willey & Sons, (1963).
  • [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.
  • [8] Ruppert, W.A.F.: On open subsemigroups of connected groups. Semigroup Forum Vol. 50, pp. 59-88, (1995).
  • [9] San Martin, L.A.B.: Invariant control sets on flag manifolds. Math. Control Signals Systems 6, pp. 41-61, (1993).
  • [10] San Martin, L.A.B.: Semigroups of local homeomorphisms. Submitted.
  • [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).
  • [12] San Martin, L.A.B. ; Tonelli, P.A.: Semigroup actions on homogeneous spaces. Semigroup Forum 50, pp. 59-88, (1995).