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Эта публикация цитируется в 10 научных статьях (всего в 10 статьях)
On the Existence of Invariant Tori in Nearly-Integrable Hamiltonian Systems With Finitely Differentiable Perturbations
J. Albrecht Friedrichshof, Köln, 50997 Germany
Аннотация:
We prove the existence of invariant tori in Hamiltonian systems, which are analytic and integrable except a $2n$-times continuously differentiable perturbation ($n$ denotes the number of the degrees of freedom), provided that the moduli of continuity of the $2n$-th partial derivatives of the perturbation satisfy a condition of finiteness (condition on an integral), which is more general than a Hölder condition. So far the existence of invariant tori could be proven only under the condition that the $2n$-th partial derivatives of the perturbation are Hölder continuous.
Ключевые слова:
nearly integrable Hamiltonian systems, KAM theory, perturbations, small divisors, Celestial Mechanics, quasi-periodic motions, invariant tori, trigonometric approximation in several variables, Holder condition.
Поступила в редакцию: 17.11.2006 Принята в печать: 02.05.2007
Образец цитирования:
J. Albrecht, “On the Existence of Invariant Tori in Nearly-Integrable Hamiltonian Systems With Finitely Differentiable Perturbations”, Regul. Chaotic Dyn., 12:3 (2007), 281–320
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd625 https://www.mathnet.ru/rus/rcd/v12/i3/p281
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