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Normal Forms of Equivariant Functions

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Abstract

Equivariant analogues of the Morse lemma with parameters and the theorem on the normal form of a semi-quasi-homogeneous function are proved.

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References

  1. W. Domitrz, M. Manoel, P. Rios de M., “The Wigner Caustic on Shell and Singularities of Odd Functions,” Geometry and Phys. 71, 58 (2013).

    Article  MathSciNet  Google Scholar 

  2. E. A. Astashov, “Classification of Z3-Equivariant Simple Function Germs,” Matem. Zametki 105 (2), 163 (2019) [Math. Notes 105 (2), 161 (2019)].

    Article  MathSciNet  Google Scholar 

  3. E. A. Astashov, “Classification of Singularities Being Equivariant Simple Relative to Cyclic Group Representations,” Vestn. Udmurt. Univ., Matem. Mekhan. Komput. Nauki 26 (2), 155 (2016).

    Article  MathSciNet  Google Scholar 

  4. S. Bochner, “Compact Groups of Differentiable Transformations,” Ann. Math. 46, 372 (1945).

    Article  MathSciNet  Google Scholar 

  5. E. B. Vinberg and V. L. Popov, “Theory of Invariants, Algebraic Geometry 4,” Itogi Nauki i Tekhniki, Ser. Fundam. Naprav., 55, 137 (1989).

    MATH  Google Scholar 

  6. I. A. Proskurnin, “Equivariant Sufficiency and Stability,” Vestn. Mosk. Univ., Matem. Mekhan., No. 4, 56 (2018).

    MathSciNet  MATH  Google Scholar 

  7. V. I. Arnold, “Evolution of Wave Fronts and Morse Equivariant Lemma,” in: Selected-60 (Fasis, Moscow, 1997), pp. 289–319.

    Google Scholar 

  8. V. I. Arnold, “Normal Forms of Functions in Neighborhood of Degenerate Critical Points,” Uspekhi Matem. Nauk 29 (2), 11 (1974).

    MathSciNet  Google Scholar 

  9. V. I. Arnold, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Maps, Vol.1: The Classification of Critical Points Caustics and Wave Fronts (Nauka, Moscow, 1982; Birkhäuser, Basel, 1985).

    MATH  Google Scholar 

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Acknowledgments

The work was supported by the Russian Science Foundation (project no. 16-11-10018).

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Authors and Affiliations

  1. Moscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow, 119991, Russia

    I. A. Proskurnin

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  1. I. A. Proskurnin
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Correspondence to I. A. Proskurnin.

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Russian Text © The Author(s), 2020, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2020, Vol. 75, No. 2, pp. 52–56.

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Proskurnin, I.A. Normal Forms of Equivariant Functions. Moscow Univ. Math. Bull. 75, 83–86 (2020). https://doi.org/10.3103/S0027132220020072

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  • DOI: https://doi.org/10.3103/S0027132220020072

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