Matrix-second order differential equations and chaotic Hamiltonian systems (Q1263853)

The authors 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.