Díaz-Cano Ocaña, Antonio and Gonzalez Gascón, F. and Peralta Salas, Daniel (2007) Symmetric submersions of R-n -> R-m. Nonlinear Analysis: Theory, Methods & Applications , 67 (8). pp. 2424-2432. ISSN 0362-546X
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Official URL: http://www.sciencedirect.com/science/article/pii/S0362546X06005323
Abstract
Submersions f such that f(-1)(0) contains a given fiber F, and that are invariant under a family of vector fields s leaving F invariant, are constructed. Examples for which a submersion of this kind cannot exist are also given. In the absence of a geometric theory of submersions f invariant under s, most of our treatment is analytic.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Submersions; Symmetries |
| Subjects: | Sciences > Mathematics > Differential equations |
| ID Code: | 15013 |
| References: | V.I. Arnold, Les M´ethodes Math´ematiques de la Mécanique Classique, Mir, 1976. V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, 1983. V.I. Arnold, V.V. Kozlov, A.I. Ne˘ıshtadt, Dynamical Systems III, in: Encyclopaedia Math. Sci., vol. 3, Springer-Verlag, 1988. L. Bianchi, Lezioni Sulla Teoria dei Gruppi Continui Finiti di Trasformazioni, vol. VI, Bologna, Zanichelli, 1928. C. Chicone, P. Ehrlich, Gradient-like and integrable vector fields on R2, Manuscripta Math. 49 (1984) 141–164. A.F. Costa, F. Gonz´alez-Gasc´on, A. Gonz´alez-L´opez, On codimension one submersions of euclidean spaces, Invent. Math. 93 (1988) 545–555. M. Gromov, Partial Differential Relations, Springer-Verlag, 1986. W. Hahn, Stability of Motion, in: die Grundlehren der mathematischen Wissenschaften, Band 138, Springer-Verlag, 1967. G. Hector, W. Bouma, All open surfaces are leaves of simple foliations of R3, Nederl. Akad. Wetensch. Indag. Math. 45 (1983) 443–452. L. Markus, Parallel dynamical systems, Topology 8 (1969) 47–57. |
| Deposited On: | 25 Apr 2012 11:19 |
| Last Modified: | 11 Nov 2013 15:44 |
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