Nonintegrability of some Hamiltonian systems, scattering and analytic continuation

Details Nonintegrability of some Hamiltonian systems, scattering and analytic continuation Nonintegrability of some Hamiltonian systems, scattering and analytic continuation

Dec 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cmaph.166..255g&link_type=abstract

Communications in Mathematical Physics, vol. 166, Issue 2, p.255-277

Mathematics

Mathematical Physics

11

Scientific paper

We consider canonical two degrees of freedom analytic Hamiltonian systems with Hamiltonian functionH=1/2[p 1 2 +p 2 2 ]+U(q 1,q 2), where U(q1, q2) = 1/2[- v2q 1 2 + ω2q 2 2 ] +O(q 1 2 + q 2 2 )3/2) and ∂q2 U(q1, 0) = 0. Under some additional, not so restrictive hypothesis, we present explicit conditions for the exisstence of transversal homoclinic orbits to some periodic orbits of these systems. We use a theorem of Lerman (1991) and an analogy between one of its conditions with the usual one dimensional quantum scattering problem. The study of the scattering equation leads us to an analytic continuation problem for the solutions of a linear second order differential equation. We apply our results to some classical problems.

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