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Poincaré inverse problem and torus construction in phase space

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Pages (from-to)72-82
JournalPhysica D: Nonlinear Phenomena
Early online date26 Oct 2015
Publication statusPublished - 2016
Publication typeA1 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

Publication forum classification

Field of science, Statistics Finland