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On the stability of periodic motions of an autonomous Hamiltonian system in a critical case of the fourth-order resonanceстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 27 марта 2018 г.
- Автор: Markeev A.P.
- Журнал: Regular and Chaotic Dynamics
- Том: 22
- Номер: 7
- Год издания: 2017
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 773
- Последняя страница: 781
- DOI: 10.1134/S1560354717070012
- Аннотация: The problem of orbital stability of a periodic motion of an autonomous two-degree-of- freedom Hamiltonian system is studied. The linearized equations of perturbed motion always have two real multipliers equal to one, because of the autonomy and the Hamiltonian structure of the system. The other two multipliers are assumed to be complex conjugate numbers with absolute values equal to one, and the system has no resonances up to third order inclusive, but has a fourth-order resonance. It is believed that this case is the critical one for the resonance, when the solution of the stability problem requires considering terms higher than the fourth degree in the series expansion of the Hamiltonian of the perturbed motion. Using Lyapunov’s methods and KAM theory, sufficient conditions for stability and instability are obtained, which are represented in the form of inequalities depending on the coefficients of series expansion of the Hamiltonian up to the sixth degree inclusive.
- Добавил в систему: Зобова Александра Александровна
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