Аннотация:
We propose a new approach to the theory of normal forms for Hamiltonian systems
near a nonresonant elliptic singular point. We consider the space of all Hamiltonian functions
with such an equilibrium position at the origin and construct a differential equation in this space.
Solutions of this equation move Hamiltonian functions towards their normal forms. Shifts along
the flow of this equation correspond to canonical coordinate changes. So, we have a continuous
normalization procedure. The formal aspect of the theory presents no difficulties. As usual, the
analytic aspect and the problems of convergence of series are nontrivial.
Ключевые слова:
normal forms, Hamiltonian systems, small divisors.
D. V. Treschev, “Normalization flow in the presence of a resonance”, Изв. РАН. Сер. матем., 89:1 (2025), 184–207
С. В. Болотин, О. Э. Зубелевич, В. В. Козлов, С. Б. Куксин, А. И. Нейштадт, “Дмитрий Валерьевич Трещев (к шестидесятилетию со дня рождения)”, УМН, 80:1(481) (2025), 165–170
D. V. Treschev, “Normalization flow in the presence of a resonance”, Изв. РАН. Сер. матем., 89:1 (2025), 184–207; D. V. Treschev, “Normalization flow in the presence of a resonance”, Izv. Math., 89:1 (2025), 172–195
Д. В. Трещев, Е. И. Кугушев, Т. В. Попова, С. В. Болотин, Ю. Ф. Голубев, В. А. Самсонов, Ю. Д. Селюцкий, “Кафедра теоретической механики и мехатроники”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 2024, № 6, 103–113
D. V. Treschev, E. I. Kugushev, T. V. Shakhova, S. V. Bolotin, Yu. F. Golubev, V. A. Samsonov, Yu. D. Selyutskiy, “Chair of Theoretical Mechanics and Mechatronics”, Moscow Univ. Mech. Bull., 79:6 (2024), 200
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