Общая информация
Последний выпуск

Поиск публикаций
Поиск ссылок

Последний выпуск
Текущие выпуски
Архивные выпуски
Что такое RSS

Regul. Chaotic Dyn.:

Персональный вход:
Запомнить пароль
Забыли пароль?

Regul. Chaotic Dyn., 2013, том 18, выпуск 6, страницы 860–906 (Mi rcd172)  

Эта публикация цитируется в 10 научных статьях (всего в 10 статьях)

Aspects of the Planetary Birkhoff Normal Form

Gabriella Pinzari

Dipartimento di Matematica ed Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Monte Sant’Angelo — Via Cinthia I-80126 Napoli, Italy

Аннотация: The discovery of the Birkhoff normal form for the planetary many-body problem opened new insights and hopes for the comprehension of the dynamics of this problem. Remarkably, it allowed to give a direct proof (after the proof in [18]) of the celebrated Arnold’s Theorem [5] on the stability of planetary motions. In this paper, after reviewing the story of the proof of this theorem, we focus on technical aspects of this normal form. We develop an asymptotic formula for it that may turn to be useful in applications. Then we provide two simple applications to the three-body problem: we prove that the “density” of the Kolmogorov set of the spatial three-body problem does not depend on eccentricities and the mutual inclination but depends only on the planets’ masses and the separation among semi-axes (going in the direction of an assertion by V.I. Arnold [5]) and, using Nehorošhev Theory [33], we prove, in the planar case, stability of all planetary actions over exponentially-long times, provided meanmotion resonances are excluded. We also briefly discuss difficulties for full generalization of the results in the paper.

Ключевые слова: averaging theory, Birkhoff normal form, Nehoroshev theory, planetary many-body problem, Arnold’s Theorem on the stability of planetary motions, properly-degenerate KAM theory, steepness

Финансовая поддержка Номер гранта
European Union's Seventh Framework Programme
Research Supported by “Prin 2009 project Critical Point Theory and Perturbative Methods for Nonlinear Differential Equations” and European Research Council under FP7 project.


Список литературы: PDF файл   HTML файл

Реферативные базы данных:

Тип публикации: Статья
MSC: 34D10, 34C20, 70E55, 70F10, 70F15, 70F07, 37J10, 37J15, 37J25, 37J35, 37J40, 70K45
Поступила в редакцию: 16.07.2013
Принята в печать:04.12.2013
Язык публикации: английский

Образец цитирования: Gabriella Pinzari, “Aspects of the Planetary Birkhoff Normal Form”, Regul. Chaotic Dyn., 18:6 (2013), 860–906

Цитирование в формате AMSBIB
\by Gabriella Pinzari
\paper Aspects of the Planetary Birkhoff Normal Form
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 6
\pages 860--906

Образцы ссылок на эту страницу:

    ОТПРАВИТЬ: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    Эта публикация цитируется в следующих статьяx:
    1. Gabriella Schirinzi, Massimiliano Guzzo, “Numerical Verification of the Steepness of Three and Four Degrees of Freedom Hamiltonian Systems”, Regul. Chaotic Dyn., 20:1 (2015), 1–18  mathnet  crossref  mathscinet  zmath  adsnasa
    2. M. Guzzo, “The Nekhoroshev theorem and long-term stabilities in the solar system”, Serb. Astron. J., 190 (2015), 1–10  crossref  isi  scopus
    3. G. Pinzari, “Canonical coordinates for the planetary problem”, Acta Appl. Math., 137:1 (2015), 205–232  crossref  mathscinet  zmath  isi
    4. G. Pinzari, “Global Kolmogorov tori in the planetary $N$-body problem. Announcement of result”, Electron. Res. Announc. Math. Sci., 22 (2015), 55–75  crossref  mathscinet  zmath  isi
    5. Massimiliano Guzzo, Elena Lega, “The Nekhoroshev Theorem and the Observation of Long-term Diffusion in Hamiltonian Systems”, Regul. Chaotic Dyn., 21:6 (2016), 707–719  mathnet  crossref  mathscinet
    6. A. Fortunati, S. Wiggins, “Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations”, Celest. Mech. Dyn. Astron., 125:2 (2016), 247–262  crossref  mathscinet  zmath  isi  scopus
    7. M. Guzzo, L. Chierchia, G. Benettin, “The steep Nekhoroshev's theorem”, Commun. Math. Phys., 342:2 (2016), 569–601  crossref  mathscinet  zmath  isi  scopus
    8. Mikhail B. Sevryuk, “Families of Invariant Tori in KAM Theory: Interplay of Integer Characteristics”, Regul. Chaotic Dyn., 22:6 (2017), 603–615  mathnet  crossref  mathscinet
    9. G. Pinzari, “On the co-existence of maximal and whiskered tori in the planetary three-body problem”, J. Math. Phys., 59:5 (2018), 052701  crossref  mathscinet  zmath  isi  scopus
    10. G. Pinzari, Perihelia reduction and global Kolmogorov tori in the planetary problem, Mem. Am. Math. Soc., 255, no. 1218, 2018, v+92 pp.  crossref  mathscinet  isi  scopus
  • Просмотров:
    Эта страница:66
    Обратная связь:
     Пользовательское соглашение  Регистрация  Логотипы © Математический институт им. В. А. Стеклова РАН, 2020