On Hamiltonian flows whose orbits are straight lines
Dynamical Systems
2013-04-12 v1
Abstract
We consider real analytic Hamiltonians whose flow depends linearly on time. Trivial examples are Hamiltonians that do not depend on the coordinate . By a theorem of Moser, every polynomial Hamiltonian of degree 3 reduces to such a -independent Hamiltonian via a linear symplectic change of variables. We show that such a reduction is impossible, in general, for polynomials of degree 4 or higher. 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.
Cite
@article{arxiv.1304.3377,
title = {On Hamiltonian flows whose orbits are straight lines},
author = {Hans Koch and Héctor E. Lomelí},
journal= {arXiv preprint arXiv:1304.3377},
year = {2013}
}