Journal of Statistical Physics

, Volume 52, Issue 1–2, pp 471–477 | Cite as

A remark on the KAM theorem applied to a four-vortex system

  • Alessandra Celletti
  • Corrado Falcolini
Short Communications

Abstract

We consider a planar four-vortex system with unit intensities and apply the KAM theorem for two-dimensional tori with fixed frequency. We obtain a rigorous lower bound for the stochasticity threshold of the torus with rotation numberω=(√5—1)/2 and compare our result with numerical experiments.

Key words

KAM theory quasiperiodic motions four-vortex system stochasticity threshold 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. L. Ziglin,Sov. Math. Dokl. 21:296–299 (1980).Google Scholar
  2. 2.
    K. M. Khanin,Physica 4D:261–269 (1982).Google Scholar
  3. 3.
    C. Marchioro and M. Pulvirenti,Vortex Methods in Two Dimensional Fluid Dynamics (KLIM, 1983).Google Scholar
  4. 4.
    A. Celletti and L. Chierchia,J. Math. Phys. 28 (1987).Google Scholar
  5. 5.
    A. Celletti, C. Falcolini, and A. Porzio,Ann. Inst. Henri Poincaré 47 (1987).Google Scholar
  6. 6.
    A. Celletti and L. Chierchia, Construction of analytic KAM surfaces and effective stability bounds; to appear inComm. Math. Phys. Google Scholar
  7. 7.
    H. Aref and N. Pomphrey,Proc. R. Soc. Lond. A 380:359–387 (1982).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Alessandra Celletti
    • 1
  • Corrado Falcolini
    • 2
  1. 1.Forschungsinstitut für Mathematik ETH-ZentrumZurichSwitzerland
  2. 2.Dipartimento di MatematicaII Universitá di RomaRomeItaly

Personalised recommendations