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Poincaré inverse problem and torus construction in phase space

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Poincaré inverse problem and torus construction in phase space. / Laakso, Teemu; Kaasalainen, Mikko.

In: Physica D: Nonlinear Phenomena, Vol. 315, 2016, p. 72-82.

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Laakso, Teemu ; Kaasalainen, Mikko. / Poincaré inverse problem and torus construction in phase space. In: Physica D: Nonlinear Phenomena. 2016 ; Vol. 315. pp. 72-82.

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@article{06827754d5ed443aa4ee7c13fc59a267,
title = "Poincar{\'e} inverse problem and torus construction in phase space",
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.",
keywords = "Near integrability, Invariant torus, Torus construction, Surface construction in N dimensions, Poincare inverse problem, Geometric inverse problems",
author = "Teemu Laakso and Mikko Kaasalainen",
year = "2016",
doi = "10.1016/j.physd.2015.10.011",
language = "English",
volume = "315",
pages = "72--82",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",

}

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TY - JOUR

T1 - Poincaré inverse problem and torus construction in phase space

AU - Laakso, Teemu

AU - Kaasalainen, Mikko

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Near integrability

KW - Invariant torus

KW - Torus construction

KW - Surface construction in N dimensions

KW - Poincare inverse problem

KW - Geometric inverse problems

U2 - 10.1016/j.physd.2015.10.011

DO - 10.1016/j.physd.2015.10.011

M3 - Article

VL - 315

SP - 72

EP - 82

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

ER -