Abstract:
We prove an estimate for the number of linear commuting symmetry fields of systems of differential equations reduced to the Poincaré–Dulac normal form. We also show that if there is a complete set of commuting analytic symmetry fields with independent linear parts, then the transformation to the normal form is given by convergent power series.
Keywords:
resonant normal form, Poincaré–Dulac theorem, symmetry fields, Hamiltonian systems.
Citation:
V. V. Kozlov, “On the Theory of Normal Forms”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024, 124–127; Proc. Steklov Inst. Math., 327 (2024), 114–117
\Bibitem{Koz24}
\by V.~V.~Kozlov
\paper On the Theory of Normal Forms
\inbook Mathematical Aspects of Mechanics
\bookinfo Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 327
\pages 124--127
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4420}
\crossref{https://doi.org/10.4213/tm4420}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 327
\pages 114--117
\crossref{https://doi.org/10.1134/S0081543824060105}
Citation in format AMSBIB
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