Download PDF - Classification of relative minima singularitiesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Classification of relative minima singularities

Authors 1, 2

Affiliations

  1. Vladimir State University, Gorkiĭ, str. 87, 600026 Vladimir, Russia
  2. Moscow Aviation Institute, Volokolamskoe sh. 4, 125871 Moscow, Russia

Bibliography

  1. V. I. Arnol'd, S. M. Guseĭn-Zade, A. N. Varchenko, Singularities of Differentiable Maps I, Monogr. Math. 82, Birkhäuser, Boston, 1985.
  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. 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.
  4. J. Damon, The unfolding and determinacy theorems for subgroups of A and K, Mem. Amer. Math. Soc. 50 (1984), no. 306.
  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.
  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.
  7. M. Giusti, Classification des singularités isolées d'intersections complètes simples, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), A167-A170.
  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.
  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. 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.
  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.
  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.
Banach Center Publications
1999/50/1
Export to PBN, Opens in new tab
Pages:
75-90
Main language of publication
English
Published
1999
Exact and natural sciences