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Uspekhi Mat. Nauk, 1978, Volume 33, Issue 5(203), Pages 91–105 (Mi umn3521)  

This article is cited in 61 scientific papers (total in 62 papers)

Critical points of functions on a manifold with boundary, the simple Lie groups $B_k$, $C_k$, and $F_4$ and singularities of evolutes

V. I. Arnol'd


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English version:
Russian Mathematical Surveys, 1978, 33:5, 99–116

Bibliographic databases:

UDC: 517.5
MSC: 58K05, 58K60, 58K10, 58J55, 22Exx
Received: 05.06.1978

Citation: V. I. Arnol'd, “Critical points of functions on a manifold with boundary, the simple Lie groups $B_k$, $C_k$, and $F_4$ and singularities of evolutes”, Uspekhi Mat. Nauk, 33:5(203) (1978), 91–105; Russian Math. Surveys, 33:5 (1978), 99–116

Citation in format AMSBIB
\Bibitem{Arn78}
\by V.~I.~Arnol'd
\paper Critical points of functions on a manifold with boundary, the simple
Lie groups $B_k$, $C_k$, and $F_4$ and singularities of evolutes
\jour Uspekhi Mat. Nauk
\yr 1978
\vol 33
\issue 5(203)
\pages 91--105
\mathnet{http://mi.mathnet.ru/umn3521}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=511883}
\zmath{https://zbmath.org/?q=an:0408.58009|0415.58004}
\transl
\jour Russian Math. Surveys
\yr 1978
\vol 33
\issue 5
\pages 99--116
\crossref{https://doi.org/10.1070/RM1978v033n05ABEH002515}


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    1. O. V. Lyashko, “The geometry of bifurcation diagrams”, Russian Math. Surveys, 34:3 (1979), 209–210  mathnet  crossref  mathscinet  zmath
    2. V. I. Arnol'd, “Indices of singular points of 1-forms on a manifold with boundary, convolution of invariants of reflection groups, and singular projections of smooth surfaces”, Russian Math. Surveys, 34:1 (1979), 1–42  mathnet  crossref  mathscinet  zmath
    3. V. I. Matov, “Unimodal germs of functions on a manifold with a boundary”, Funct. Anal. Appl., 14:1 (1980), 55–57  mathnet  crossref  mathscinet  zmath
    4. A. B. Givental', “Displacement of invariants of groups that are generated by reflections and are connected with simple singularities of functions”, Funct. Anal. Appl., 14:2 (1980), 81–89  mathnet  crossref  mathscinet  zmath
    5. V. V. Goryunov, “Geometry of bifurcation diagrams of simple projections onto the line”, Funct. Anal. Appl., 15:2 (1981), 77–82  mathnet  crossref  mathscinet  zmath  isi
    6. Ian Stewart, “Applications of catastrophe theory to the physical sciences”, Physica D: Nonlinear Phenomena, 2:2 (1981), 245  crossref
    7. G. Dangelmayr, W. Güttinger, “Topological approach to remote sensing”, Geophys J Int, 71:1 (1982), 79  crossref  zmath  adsnasa  isi
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    9. O. V. Lyashko, “Primechanie k state D. Makkeya “Grafy, osobennosti i konechnye gruppy””, UMN, 38:3(231) (1983), 162–164  mathnet  mathscinet  zmath
    10. V. V. Goryunov, “Bifurcation diagrams of some simple and quasihomogeneous singularities”, Funct. Anal. Appl., 17:2 (1983), 97–108  mathnet  crossref  mathscinet  zmath  isi
    11. O. V. Lyashko, “Classification of critical points of functions on a manifold with singular boundary”, Funct. Anal. Appl., 17:3 (1983), 187–193  mathnet  crossref  mathscinet  zmath  isi
    12. O. P. Shcherbak, “Singularities of families of evolvents in the neighborhood of an inflection point of the curve, and the group $H_3$ generated by reflections”, Funct. Anal. Appl., 17:4 (1983), 301–303  mathnet  crossref  mathscinet  zmath  isi
    13. I. G. Shcherbak, “Duality of boundary singularities”, Russian Math. Surveys, 39:2 (1984), 195–196  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. I. G. Shcherbak, “Focal set of a surface with boundary, and caustics of groups generated by reflections $B_k$, $C_k$, and $F_4$”, Funct. Anal. Appl., 18:1 (1984), 84–85  mathnet  crossref  mathscinet  zmath  isi
    15. A. N. Varchenko, S. V. Chmutov, “Finite irreducible groups, generated by reflections, are monodromy groups of suitable singularities”, Funct. Anal. Appl., 18:3 (1984), 171–183  mathnet  crossref  mathscinet  zmath  isi
    16. G. G. Ilyuta, “Monodromy and vanishing cycles of boundary singularities”, Funct. Anal. Appl., 19:3 (1985), 173–182  mathnet  crossref  mathscinet  zmath  isi
    17. O. P. Shcherbak, “Wavefronts and reflection groups”, Russian Math. Surveys, 43:3 (1988), 149–194  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    18. A. B. Givental', “Twisted Picard–Lefschetz formulas”, Funct. Anal. Appl., 22:1 (1988), 10–18  mathnet  crossref  mathscinet  zmath  isi
    19. V. V. Goryunov, “Projection and vector fields, tangent to the discriminant of a complete intersection”, Funct. Anal. Appl., 22:2 (1988), 104–113  mathnet  crossref  mathscinet  zmath  isi
    20. Yu. I. Sapronov, “Angular singularities and multidimensional assemblies”, Funct. Anal. Appl., 22:3 (1988), 242–244  mathnet  crossref  mathscinet  zmath  isi
    21. J.W. Bruce, R.M. Roberts, “Critical points of functions on analytic varieties”, Topology, 27:1 (1988), 57  crossref
    22. Yu. I. Sapronov, “Semiregular corner singularities of smooth functions”, Math. USSR-Sb., 68:1 (1991), 151–163  mathnet  crossref  mathscinet  zmath  isi
    23. V. V. Goryunov, “Monodromy of the image of the mapping $\mathbb{C}^2\to\mathbb{C}^3$”, Funct. Anal. Appl., 25:3 (1991), 174–180  mathnet  crossref  mathscinet  zmath  isi
    24. V. M. Zakalyukin, R. M. Roberts, “On stable singular Lagrangian varieties”, Funct. Anal. Appl., 26:3 (1992), 174–178  mathnet  crossref  mathscinet  zmath  isi
    25. V. I. Arnol'd, “The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups”, Russian Math. Surveys, 47:1 (1992), 1–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    26. G. G. Ilyuta, “Monodromy groups of boundary singularities”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 23–34  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    27. G. G. Ilyuta, “The A'Campo Theorem on the Discriminant”, Funct. Anal. Appl., 28:2 (1994), 85–91  mathnet  crossref  mathscinet  zmath  isi
    28. A. Szpirglas, “Boundary Singularities and Symmetric Boundary Singularities”, Funct. Anal. Appl., 28:2 (1994), 137–139  mathnet  crossref  mathscinet  zmath  isi
    29. D. V. Anosov, A. A. Bolibrukh, V. A. Vassiliev, A. M. Vershik, A. A. Gonchar, M. L. Gromov, S. M. Gusein-Zade, V. M. Zakalyukin, Yu. S. Ilyashenko, V. V. Kozlov, M. L. Kontsevich, Yu. I. Manin, A. I. Neishtadt, S. P. Novikov, Yu. S. Osipov, M. B. Sevryuk, Ya. G. Sinai, A. N. Tyurin, L. D. Faddeev, B. A. Khesin, A. G. Khovanskii, “Vladimir Igorevich Arnol'd (on his 60th birthday)”, Russian Math. Surveys, 52:5 (1997), 1117–1139  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    30. V. V. Goryunov, “Unitary reflection groups associated with singularities of functions with cyclic symmetry”, Russian Math. Surveys, 54:5 (1999), 873–893  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    31. D. F. Scofield, “Quantum dynamical manifolds 5. Hydrogen mass-spacetime”, Int J Quantum Chem, 80:3 (2000), 369  crossref  isi
    32. I. G. Shcherbak, “Noncrystallographic Coxeter Groups and Boundary Singularities”, Funct. Anal. Appl., 35:2 (2001), 158–160  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    33. Slodowy P., “Simple singularities and complex reflections”, New Developments in Singularity Theory, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 21, 2001, 329–348  isi
    34. V. D. Sedykh, “Resolution of Corank $1$ Singularities of a Generic Front”, Funct. Anal. Appl., 37:2 (2003), 123–133  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    35. J. W. Bruce, “On families of symmetric matrices”, Mosc. Math. J., 3:2 (2003), 335–360  mathnet  mathscinet  zmath  elib
    36. B. M. Darinskii, Yu. I. Sapronov, S. L. Tsarev, “Bifurcations of extremals of Fredholm functionals”, Journal of Mathematical Sciences, 145:6 (2007), 5311–5453  mathnet  crossref  mathscinet  zmath  elib
    37. V. D. Sedykh, “On the topology of stable corank 1 singularities on the boundary of a connected component of the complement to a front”, Sb. Math., 195:8 (2004), 1165–1203  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    38. V. V. Goryunov, V. M. Zakalyukin, “On Stability of Projections of Lagrangian Varieties”, Funct. Anal. Appl., 38:4 (2004), 249–255  mathnet  crossref  crossref  mathscinet  zmath  isi
    39. Sunayana Ghosh, Joachim H. Rieger, “Singularities of secant maps of immersed surfaces”, Geom Dedicata, 121:1 (2007), 73  crossref  mathscinet  isi
    40. V. D. Sedykh, “Resolution of corank 1 singularities in the image of a stable smooth map to a space of higher dimension”, Izv. Math., 71:2 (2007), 391–437  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    41. Proc. Steklov Inst. Math., 258 (2007), 44–52  mathnet  crossref  mathscinet  zmath  elib
    42. V. D. Sedykh, “On the Coexistence of Corank 1 Multisingularities of a Stable Smooth Mapping of Equidimensional Manifolds”, Proc. Steklov Inst. Math., 258 (2007), 194–217  mathnet  crossref  mathscinet  zmath  elib  elib
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    44. M. D. Garay, “Vanishing cycles in complex symplectic geometry”, Mosc. Math. J., 8:1 (2008), 73–90  mathnet  mathscinet  zmath
    45. Dolgachev, IV, “Reflection groups in algebraic geometry”, Bulletin of the American Mathematical Society, 45:1 (2008), 1  crossref  mathscinet  zmath  isi
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    47. Proc. Steklov Inst. Math., 267 (2009), 91–103  mathnet  crossref  mathscinet  zmath  isi  elib
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