On the principle of stability of invariance of physical systems

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1. [1] H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste, Paris, 1899. 
2. [2] R. Abraham and J. Marsden, Foundation of Mechanics, Benjamin, New York, 1967. 
3. [3] We do not list papers because of extreamly large numbers of papers in this field. 
4. [4] R. Thom, Stabilité Structurelle et Morphogenèse, Benjamin, 1972 and reference there in. Zbl0294.92001MR488155
5. [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. Zbl0144.46201
6. [6] K.T. Shah, Topics in bifurcation theory, Seminar report, Clausthal, 1973. 
7. [7] K.T. Shah, Reports on Math. Phys., t. 6, 1974, p. 171. Zbl0314.17011MR385018
8. [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. [9] R. Richardson, Jour. of Diff. Geom., t. 3, 1969, p. 289. Zbl0215.38603
10. [10] R. Richardson, Proceedings of Symp. on Transformation Groups, Edited by P. Mostert, p. 429, Springer-Verlag, 1967. MR244439
11. [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. MR142859
12. [12] E.P. Wigner and E. Inönü, Proc. Natl. Acad. Sci (USA), t. 39, 1953, p. 510. Zbl0050.02601MR55352