Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Mouvement moyen et système dynamique gaussien
Download PDF
Download PDF
  • Published: 01 March 1995

Mouvement moyen et système dynamique gaussien

  • Thierry de la Rue1 

Probability Theory and Related Fields volume 102, pages 45–56 (1995)Cite this article

  • 103 Accesses

  • 4 Citations

  • Metrics details

Summary

In the situation of the classical mean motion, we haven planets moving in the plane, planetk+1 being a satellite of planetk. A classcal result then states that planetn has a mean motion,i.e. its mean angular speed between time 0 and timet has a limit whent→∞. We show in this article that any real gaussian dynamical system can be interpreted as the limit of this situation, whenn→∞. From a given nonatomic probability measure σ on [0,π], we construct a transformationT of the complex brownian path (B u)0≤u≤1 which preserves Wiener measure.T is defined as the limit of a sequenceT n, whereT n acts as the motion of 2n planets. In this way we get a real gaussian dynamical system, whose spectral measure is the symetric probability on [-π,π] obtained from σ. The transformationT can be inserted in a flow (T t) t∈ℝ, and the “orbits”t↦Z t=B 1○T t still have almost surely a mean motion, which is the mean of σ.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Références

  1. Cornfeld, I.P., Fomin, S.V., Sinai, Ya.G.: Ergodic Theory (Grundlernen Math. Wiss. 245) Berlin Heidelberg New York: Springer 1982

    MATH  Google Scholar 

  2. Jessen, B., Tornehave, H.: Mean motion and zeros of almost periodic functions. Acta Math.77, 138–279 (1945)

    Article  MathSciNet  MATH  Google Scholar 

  3. Lagrange, L.: Théorie des variations séculaires des éléments des planètes I et II. In: (Euvres 5 (pp. 123–344) Nouveaux Mémoires de l'Académie de Berlin 1781

  4. Levy, P.: Le mouvement brownien plan. Am. J. Math.62, 487–550 (1940)

    Article  MathSciNet  MATH  Google Scholar 

  5. Sternberg, S.: Celestial Mecanics. New York Amsterdam: Benjamin 1969

    Google Scholar 

  6. Weyl, H.: Mean motion. Am. J. Math.60, 889–896 (1938)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, URA CNRS 1378, Université de Rouen, F-76821, Mont-Saint-Aignan Cedex, France

    Thierry de la Rue

Authors
  1. Thierry de la Rue
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

de la Rue, T. Mouvement moyen et système dynamique gaussien. Probab. Theory Relat. Fields 102, 45–56 (1995). https://doi.org/10.1007/BF01295220

Download citation

  • Received: 29 November 1993

  • Revised: 23 November 1994

  • Published: 01 March 1995

  • Issue Date: March 1995

  • DOI: https://doi.org/10.1007/BF01295220

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Mathematics Subject Classification

  • 28D99
  • 60J65
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature