Poincar\'e inverse problem and torus construction in phase space
Mathematical Physics
2014-03-04 v1 math.MP
Abstract
The phase space of an integrable Hamiltonian system is foliated by invariant tori. For an arbitrary Hamiltonian H such a foliation may not exist, but we can artificially construct one through a parameterised family of surfaces, with the intention of finding, in some sense, the closest integrable approximation to H. This is the Poincar\'e inverse problem (PIP). In this paper, we review the available methods of solving the PIP and present a new iterative approach which works well for the often problematic thin orbits.
Cite
@article{arxiv.1403.0395,
title = {Poincar\'e inverse problem and torus construction in phase space},
author = {Teemu Laakso and Mikko Kaasalainen},
journal= {arXiv preprint arXiv:1403.0395},
year = {2014}
}
Comments
submitted to Inverse Probl. Imag. in Dec 2013