Relative invariance for monoid actions
-
Braga Barros, Carlos J. [1]
-
[1] Universidade Estadual de Maringá
Universidade Estadual de Maringá
Brasil
-
- Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 20, Nº. 3, 2001, págs. 281-294
- Idioma: inglés
- DOI: 10.4067/S0716-09172001000300002
- Enlaces
-
Resumen
Let S be a topological monoid acting on the topological space M. Let J be a subset of M. Our purpose here is to study the subsets of M which correspond, under the action of S, to the relative (with respect to J) invariant control sets for control systems (see [4] section 3.3). The relation x ∼ y if y ∈ cl(Sx) and x ∈ cl(Sy) is an equivalence relation and the classes with respect to this relation with nonempty interior in M are the control sets for the action of S. It is given conditions for the existence and uniqueness of relative invariant classes. As it was done for the control sets, we define an order in the classes and relate it to the relative invariant classes. We also show under certain condition that the relative invariant classes are relatively closed in J.
-
Referencias bibliográficas
- Citas [1] Colonius, F. and Kliemann, W.: Linear control semigroups acting on projective spaces. Journal of Dynamics and Differential Equations,...
- [2] Colonius, F. and Kliemann,W.: Some aspects of control systems as dynamical systems. Journal of Dynamics and Differential Equations, vol....
- [3] Colonius, F. and Kliemann, W.: The Lyapunov spectrum of families of time-varying matrices. Transactions of the American Mathematical Society,...
- [4] Colonius, F. and Kliemann, W.: “The dynamics of control”. Birkhäuser, Boston (2000).
- [5] Gottschalk, W.H. and Heldlund, G. A.: “Topological Dynamics”. American Mathematical Society, Providence, Rhode Island, 1955.
- [6] San Martin,L.A.B, and Tonelli, P.A.: Semigroup actions on homogeneous spaces. Semigroup Forum, vol. 50 (1995) 59-88.
- [7] San Martin,L.A.B.: “Control sets and semigroups in semi-simple Lie groups”. In Semigroups in algebra, geometry and analysis. Gruyter Verlag,...
- [8] San Martin L.A.B.: Order and domains of attraction of control sets in flag manifolds. Journal of Lie Theory , vol. 8, (1998) 111-128.
- [9] Ruppert, W.: “Compact Semitopological Semigroups: An Intrisic Theory”. Lecture Notes in Mathematics 1079, Springer Verlag, Berlin, Heidelberg,...
