Skip to main content
SpringerLink
Log in

Small denominators and stability problems in classical and celestial mechanics

  • Chapter
Collected Works

Part of the book series: Vladimir I. Arnold - Collected Works ((ARNOLD,volume 1))

  • 3556 Accesses

Abstract

§ 1. Вопросы устойчивости, связанные с расходимостью рядов теории возмущений, давно занимают математиков [1-6]. В последние годы в этой области достигнут некоторый прогресс. Цель настоящего сообщения - изложить результаты и методы недавних исследований поведения решений дифференциальных уравнений динамиеи на бесконечном промежутке времени [7-10].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

ЛИТЕРАТУРА

  1. P.S. Laplace. Traite de mechanique celeste, I-V. Paris. 1799-1827.

    Google Scholar 

  2. --

    Google Scholar 

  3. H. Poincare. Les methodes nouvelles de la mechanique celeste. I-III Paris, 1892-1899

    Google Scholar 

  4. C.L. Charlier. Die Mechanik des Himmels. I-II. Leipzig. 1902-1907

    Google Scholar 

  5. --

    Google Scholar 

  6. --

    Google Scholar 

  7. --

    Google Scholar 

  8. --

    Google Scholar 

  9. --

    Google Scholar 

  10. --

    Google Scholar 

  11. --

    Google Scholar 

  12. Б о р н ..Лекции по атомнои .\IехаIIике, 1. К.иев, 1934.

    Google Scholar 

  13. К. Jl. :3 и г е л ь. Сб. переводов «JVlатемаТlп<а>1, 5, 1961, 2.

    Google Scholar 

  14. C. L. Siegel. Ann. Math., 43, 1942, 4.

    Google Scholar 

  15. A. Finzi. Ann. Ecole Norm. Sup., 67, 1950, 3.

    MathSciNet  Google Scholar 

  16. A. Finzi. Ann. Ecole Norm. Sup.,69. 19'52, 3,

    Google Scholar 

  17. А.. Е. Г е J1 ь М а н. JJ:AH СССР, 116, 1957, 4.

    Google Scholar 

  18. В. i1. А Р н о .п ьд. I'Iзв. А.Н СССР, сер. матем., 25, 1961, 1

    Google Scholar 

  19. Л1. J1 е о н т о в и ч. ДАН СССР, 143, 1962, 3.

    Google Scholar 

  20. ,v1 о :3 е р. f\!\ате\fтаТJlка,сб. Пf:'реводов, 6, 1962,

    Google Scholar 

Download references

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, 94720-3840, Berkeley, CA, USA

    Alexander B. Givental

  2. Department of Mathematics, University of Toronto, M5S 3G3, Toronto, ON, Canada

    Boris A. Khesin

  3. Control & Dynamical Systems and Applied & Computational Mathematics, California Institute of Technology, 91125-8100, Pasadena, CA, USA

    Jerrold E. Marsden

  4. Department of Mathematics, University of North Carolina, 27599-3250, Chapel Hill, NC, USA

    Alexander N. Varchenko

  5. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russian Federation

    Oleg Ya. Viro

  6. Institute of Mathematical Sciences, Stony Brook University, 11794-3660, Stony Brook, NY, USA

    Vladimir M. Zakalyukin

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2009). Small denominators and stability problems in classical and celestial mechanics. In: Givental, A., et al. Collected Works. Vladimir I. Arnold - Collected Works, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01742-1_22

Download citation

Publish with us

Policies and ethics

Search

Navigation