On the principle of stability of invariance of physical systems
Tahir Shah, K.
Annales de l'I.H.P. Physique théorique, Tome 25 (1976), p. 177-182 / Harvested from Numdam
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Publié le : 1976-01-01
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     author = {Tahir Shah, K.},
     title = {On the principle of stability of invariance of physical systems},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {25},
     year = {1976},
     pages = {177-182},
     mrnumber = {424095},
     zbl = {0388.58022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1976__25_2_177_0}
}

Tahir Shah, K. On the principle of stability of invariance of physical systems. Annales de l'I.H.P. Physique théorique, Tome 25 (1976) pp. 177-182. http://gdmltest.u-ga.fr/item/AIHPA_1976__25_2_177_0/

[1] H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste, Paris, 1899.

[2] R. Abraham and J. Marsden, Foundation of Mechanics, Benjamin, New York, 1967.

[3] We do not list papers because of extreamly large numbers of papers in this field.

[4] R. Thom, Stabilité Structurelle et Morphogenèse, Benjamin, 1972 and reference there in. | MR 488155 | Zbl 0294.92001

[5] H.D. Doebner, Nouvo Cim., A49, 1967, p. 306; Jour. of Math. Phys., t. 9, 1968, p. 1638 and t. 11, 1970, p. 1463. | Zbl 0144.46201

[6] K.T. Shah, Topics in bifurcation theory, Seminar report, Clausthal, 1973.

[7] K.T. Shah, Reports on Math. Phys., t. 6, 1974, p. 171. | MR 385018 | Zbl 0314.17011

[8] R. Thom, Symmetries gained and lost, Proceedings of III GIFT Seminars in Theor. Phys., Madrid, 1972 ; see also L. Michel, Geometrical aspects of symmetry breaking, same proceedings.

[9] R. Richardson, Jour. of Diff. Geom., t. 3, 1969, p. 289. | Zbl 0215.38603

[10] R. Richardson, Proceedings of Symp. on Transformation Groups, Edited by P. Mostert, p. 429, Springer-Verlag, 1967. | MR 244439

[11] M. Peixoto, (Topology, t. 1, 1962, p. 101, Ann. of Math., t. 87, 1968, p. 422) has shown that if the dimension of the manifold is two, then the set of structurally stable vector field or dynamical system is a dense set on the set of all vector fields on this two dimensional manifold. In the case of differentiable maps i. e. C∞-maps, one can define stability as follows. Let Mn and Np be the two C∞-manifolds and let Cr (,) be the space of all maps from Mn to Np provided with the Cr-topology. A map is called stable if all'nearby maps' k are of the same type topologically as f and the diagram is commutative, i. e. fh = h'k where h and h' are ∈-homeomorphisms of Mn and Np. For a general reference, see M. Golubitsky and Guillemin, Stable mappings and their Singularities, Springer-Verlag, 1973. | MR 142859

[12] E.P. Wigner and E. Inönü, Proc. Natl. Acad. Sci (USA), t. 39, 1953, p. 510. | MR 55352 | Zbl 0050.02601