13-13 Hans Koch, Hector E. Lomeli

On Hamiltonian flows whose orbits are straight lines (251K, plain TeX) Feb 27, 13

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Abstract. We consider real analytic Hamiltonians on $ eal^n imes eal^n$ whose flow depends linearly on time. Trivial examples are Hamiltonians $H(q,p)$ that depend only on the coordinate $p\in eal^n$. By a theorem of Moser [5], every cubic Hamiltonian reduces to a Hamiltonian of this type via a linear symplectic change of variables. We show that the same does not hold for polynomials of degree $\ge 4$. But we give a condition that implies linear-symplectic conjugacy to another simple class of Hamiltonians. The condition is shown to hold for all nondegenerate Hamiltonians that are homogeneous of degree $4$.

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