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The magnetic geodesic flow in a homogeneous field on the complex projective space.
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In this article, the authors prove commutative integrability of the Hamilton system on the tangent bundle of the complex projective space whose Hamiltonian coincides with the Hamiltonian of the geodesic flow.Abstract:
We prove commutative integrability of the Hamilton system on the tangent bundle of the complex projective space whose Hamiltonian coincides with the Hamiltonian of the geodesic flow and the Poisson bracket deforms due to addition of the Fubini–Study form to the standard symplectic form.read more
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Symmetries and integrability
TL;DR: A survey on finite-dimensional integrable dynamical systems related to Hamiltonian G-actions can be found in this article, where integrability of G-invariant systems, collective motions and reduced integrabilities are studied.
Journal ArticleDOI
The magnetic geodesic flow on a homogeneous symplectic manifold
TL;DR: The non-commutative integrability of the magnetic geodesic flow defined by the Kirillov form on a coadjoint orbit of a compact semisimple Lie group was shown in this paper.
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Magnetic flows on homogeneous spaces
TL;DR: In this article, the authors consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups.
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Magnetic geodesic flows on coadjoint orbits
TL;DR: In this article, a class of completely integrable G-invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group G with magnetic field given by the Kirillov-Konstant 2-form is described.
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Magnetic Flows on Homogeneous Spaces
TL;DR: In this paper, the authors considered magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups.
References
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Integrable geodesic flows on homogeneous spaces
TL;DR: In this paper, a method for the construction of families of first integrals in involution for Hamiltonian systems which are invariant under the Hamiltonian action of a Lie group G is presented.
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