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


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 


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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

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