We present a classification of simple singularities of analytic functions of many real or complex variables possessing the evenness or oddness property in each variable. Bibliography: 16 titles.
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References
V. I. Arnol’d, “Normal forms for functions near degenerate critical points, the Weyl groups of Ak, Dk, Ek and Lagrangian singularities,” Funct. Anal. Appl. 6, 254–272 (1973).
D. Siersma, “The singularities of C∞-functions of right-codimension smaller or equal than eight,” Nederl. Akad. Wet., Proc. Ser. 76, No. 1, 31–37 (1973).
V. I. Arnol’d, “Critical points of functions on a manifold with boundary, the simple Lie groups Bk, Ck, F4 and singularities of evolutes,” Russ. Math. Surv. 33, No. 5, 99–116 (1978).
D. Siersma, “Singularities of functions on boundaries, corners, etc.,” Q. J. Math., Oxf. II. Ser. 32, No. 1, 119–127 (1981).
W. Domitrz, M. Manoel, and P. de M. Rios, “The Wigner caustic on shell and singularities of odd functions,” J. Geom. Phys. 71, 58–72 (2013).
E. A. Astashov, “On the classification of singularities that are equivariant simple with respect to representations of cyclic groups” [in Russian], Vestn. Udmurt. Univ., Mat. Mekh. Komp’yut. Nauki 26, No. 2, 155–159 (2016).
E. A. Astashov, “On the classification of function germs of two variables that are equivariant simple with respect to an action of the cyclic group of order three” [in Russian], Vestn. Samar. Univ., Estestvennonauchn. Ser. 3-4, No. 2, 7–13 (2016).
E. A. Astashov, “Classification of Z3-equivariant simple function germs,” Math. Notes 105, No. 2, 161–172 (2019).
E. Astashov, “Equivariant simple singularities and admissible sets of weights,” WSEAS Trans. Math. 17, 404–410 (2018).
V. V. Goryunov and C. E. Baines, “Cyclically equivariant function singularities and unitary reflection groups G(2m, 2, n),G9,G31,” St. Petersbg. Math. J. 11 No. 5, 761–774 (2000).
S. Bochner, “Compact groups of differentiable transformations,” Ann. Math. (2) 46, 372–381 (1945).
J. J. Duistermaat and J. A. C. Kolk, Lie Groups, Springer, Berlin (2000).
M. Giusti, “Classification des singularités isolées simples d’intersections complètes,” Proc. Symp. Pure Math. 40, Part 1, 457–494 (1983).
G. Wasserman, Classification of Singularities with Compact Abelian Symmetry, Regensburger Math. Schriften 1 (1977).
P. Slodowy, “Einige Bemerkungen zur Entfaltung symmetrischer Funktionen,” Math. Z. 158, 157–170 (1978).
J. W. Bruce, N. P. Kirk, and A. A. du Plessis, “Complete transversals and the classification of singularities,” Nonlinearity 10, No. 1, 253–275 (1997).
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Translated from Problemy Matematicheskogo Analiza 103, 2020, pp. 11-16.
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Abdrakhmanova, N.T., Astashov, E.A. Simple Singularities of Functions that are Even or Odd in Each Variable. J Math Sci 249, 827–833 (2020). https://doi.org/10.1007/s10958-020-04976-x
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DOI: https://doi.org/10.1007/s10958-020-04976-x