Generically, Arnold-Liouville Systems Cannot be Bi-Hamiltonian
Differential Geometry
2021-11-01 v2
Abstract
We state and prove that a certain class of smooth functions said to be BH-separable is a meagre subset for the Fr\'echet topology. Because these functions are the only admissible Hamiltonians for Arnold-Liouville systems admitting a bi-Hamiltonian structure, we get that, generically, Arnold-Liouville systems cannot be bi-Hamiltonian. At the end of the paper, we determine, both as a concrete representation of our general result and as an illustrative list, which polynomial Hamiltonians of the form are BH-separable.
Cite
@article{arxiv.2105.11123,
title = {Generically, Arnold-Liouville Systems Cannot be Bi-Hamiltonian},
author = {Hassan Boualem and Robert Brouzet},
journal= {arXiv preprint arXiv:2105.11123},
year = {2021}
}