Poincaré inverse problem and torus construction in phase space
Research output: Contribution to journal › Article › Scientific › peer-review
|Journal||Physica D: Nonlinear Phenomena|
|Early online date||26 Oct 2015|
|Publication status||Published - 2016|
|Publication type||A1 Journal article-refereed|
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 Poincaré 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.
- Near integrability, Invariant torus, Torus construction, Surface construction in N dimensions, Poincare inverse problem, Geometric inverse problems