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Matrix-second order differential equations and chaotic Hamiltonian systems

  • A. Celletti
  • J. P. Francoise
Brief Reports

Abstract

We consider matrix-second order differential equations which are perturbations of the harmonic flow on the space of matrices. Experimental evidence of the non integrability of the two degrees of freedom Hamiltonian system provides an indication of the non existence of a Lax pair with commuting eigenvalues for perturbations of order six. This shows the specificity of quartic perturbations for which such a Lax pair was precedently obtained.

Keywords

Differential Equation Experimental Evidence Mathematical Method Hamiltonian System Order Differential Equation 
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Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • A. Celletti
    • 1
  • J. P. Francoise
    • 2
  1. 1.Forschungsinstitut für MathematikETH-ZentrumZürich
  2. 2.Bat. n.425, MathématiquesUniversité de Paris XIOrsay, CedexFrance

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