 1313 Hans Koch, Hector E. Lomeli
 On Hamiltonian flows whose orbits are straight lines
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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 linearsymplectic 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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