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KIAM Preprint № 65, Moscow, 2021
Authors: Bruno A.D., Batkhin A.B.
Normal form of a binary polynomial in the critical point of the second order
Abstract:
We consider a real polynomial of two variables. Its expansion in the vicinity of the zero singular point begins with the third degree form. We find its simplest forms to which this polynomial is reduced by reversible real local analytic coordinate substitutions. First, the normal forms for the cubic form are obtained using linear coordinate substitutions. There are three of them. Then three non-linear normal forms were obtained for the full polynomial. A simplification of the computation of the normal form is proposed. A meaningful example is considered.
Keywords:
cubic form, coordinate change, normal form, non-linear normalization
Publication language: russian,  pages: 20
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Bruno Alexander Dmitrievich,  orcid.org/0000-0002-7465-1258KIAM RAS
  • Batkhin Alexander Borisovich,  orcid.org/0000-0001-8871-4697KIAM RAS