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Integrable magnetic geodesic flows on Lie groups

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arxiv 1111.0726 v1 pith:AC554X6C submitted 2011-11-03 math-ph math.MP

Alexey A. Magazev , Igor V. Shirokov , Yuriy Y. Yurevich This is my paper · ORCID
classification math-phmath.MP
keywords flowsgeodesicalgebrascocyclesgroupsintegrablemagneticalgebra
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Right-invariant geodesic flows on manifolds of Lie groups associated with 2-cocycles of corresponding Lie algebras are discussed. Algebra of integrals of motion for magnetic geodesic flows is considered and necessary and sufficient condition of integrability in quadratures is formulated. Canonic forms for 2-cocycles of all 4-dimensional Lie algebras are given and integrable cases among them are separated.

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Cited by 1 Pith paper

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  1. A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions

    nlin.SI 2025-06 conditional novelty 7.0 of 10

    The paper proves complete integrability of homogeneous exact magnetic flows on spheres in all dimensions via a Lax representation.

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