Classification of relative minima singularities

 Access to full text

 Full (PDF)

1. [1] V. I. Arnol'd, S. M. Guseĭn-Zade, A. N. Varchenko, Singularities of Differentiable Maps I, Monogr. Math. 82, Birkhäuser, Boston, 1985. 
2. [2] V. I. Arnol'd, V. V. Goryunov, O. V. Lyashko and V. A. Vasil'ev, Singularity theory. II. Classification and applications, in: Dynamical Systems VIII, Encyclopaedia Math. Sci. 39, Springer, Berlin, 1993, 1-235. 
3. [3] L. N. Bryzgalova, The maximum functions of a family of functions that depend on parameters (in Russian), Funktsional. Anal. i Prilozhen. 12 (1978), no. 1, 66-67; English transl.: Functional Anal. Appl. 12 (1978), 50-51. Zbl0405.58024
4. [4] J. Damon, The unfolding and determinacy theorems for subgroups of A and K, Mem. Amer. Math. Soc. 50 (1984), no. 306. 
5. [5] A. A. Davydov, Singularities of the maximum function over a preimage, in: Geometry in Nonlinear Control and Differential Inclusions, Banach Center Publ. 32, Warsaw, 1995, 167-181. Zbl0870.58009
6. [6] A. A. Davydov, V. M. Zakalyukin, Point singularities of relative minimum on three dimensional manifold (in Russian), Trudy Mat. Inst. Steklov. 220 (1998), 113-129; English transl.: Proc. Steklov Inst. Mat. 220 (1998), 109-125. Zbl0920.58008
7. [7] M. Giusti, Classification des singularités isolées d'intersections complètes simples, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), A167-A170. Zbl0346.32015
8. [8] V. V. Goryunov, Geometry of the bifurcation diagrams of simple projections onto a line (in Russian), Funktsional. Anal. i Prilozhen. 15 (1981), no. 2, 1-8; English transl.: Functional Anal. Appl. 15 (1981), 77-82. Zbl0507.58010
9. [9] O. V. Lyashko, Classification of critical points of functions on a manifold with singular boundary (in Russian), Funktsional. Anal. i Prilozhen. 17 (1983), no. 3, 28-36; English transl.: Functional Anal. Appl. 17 (1983), 187-193. 
10. [10] V. I. Matov, Topological classification of the germs of functions of the maximum and minimax of families of functions in general position (in Russian), Uspekhi Mat. Nauk 37 (1982), no. 4, 167-168; English transl.: Russian Math. Surveys 37 (1982), no. 4, 127-128. Zbl0506.58004
11. [11] V. M. Zakalyukin, Envelopes of families of wave fronts and control theory (in Russian), Trudy Mat. Inst. Steklov. 209 (1995), 133-142; English transl.: Proc. Steklov Inst. Math. 209 (1995), 114-123. Zbl0883.93008
12. [12] V. M. Zakalyukin, Singularities of circles contact with surfaces and flags, Funktsional. Anal. i Prilozhen. 31 (1997), no. 2, 73-76; English transl.: Functional Anal. Appl. 31 (1997), 131-133.