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On the theory of normal forms
V. V. Kozlov
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Abstract:
An estimate of the number of linear commuting fields of symmetries of systems of differential equations reduced to the Poincare-Dulac normal form is proved. It is shown that if there is a complete set of commuting analytical fields of symmetries with independent linear parts, then the transformation to normal form is given by converging power series.
Keywords:
resonant normal form, the Poincare-Dulac theory, symmetry fields, hamiltonian systems
Received: May 20, 2024
Revised: May 20, 2024
Accepted: September 16, 2024
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