@article{AIHPA_1976__25_2_177_0,
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},
pages = {177--182},
publisher = {Gauthier-Villars},
volume = {25},
number = {2},
year = {1976},
zbl = {0388.58022},
mrnumber = {424095},
language = {en},
url = {http://www.numdam.org/item/AIHPA_1976__25_2_177_0/}
}
TY - JOUR AU - Tahir Shah, K. TI - On the principle of stability of invariance of physical systems JO - Annales de l'I.H.P. Physique théorique PY - 1976 DA - 1976/// SP - 177 EP - 182 VL - 25 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1976__25_2_177_0/ UR - https://zbmath.org/?q=an%3A0388.58022 UR - https://www.ams.org/mathscinet-getitem?mr=424095 LA - en ID - AIHPA_1976__25_2_177_0 ER -
Tahir Shah, K. On the principle of stability of invariance of physical systems. Annales de l'I.H.P. Physique théorique, Tome 25 (1976) no. 2, pp. 177-182. http://www.numdam.org/item/AIHPA_1976__25_2_177_0/
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[2] and , Foundation of Mechanics, Benjamin, New York, 1967.
[3] We do not list papers because of extreamly large numbers of papers in this field.
[4] , Stabilité Structurelle et Morphogenèse, Benjamin, 1972 and reference there in. | MR 488155 | Zbl 0294.92001
[5] , Nouvo Cim., A49, 1967, p. 306; Jour. of Math. Phys., t. 9, 1968, p. 1638 and t. 11, 1970, p. 1463. | Zbl 0144.46201
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[11] , (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] and , Proc. Natl. Acad. Sci (USA), t. 39, 1953, p. 510. | MR 55352 | Zbl 0050.02601
