A. V. Bolsinov, B. Jovanović, “Integrable geodesic flows on homogeneous spaces”, Sb. Math., 192:7 (2001), 951

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Sbornik: Mathematics, 2001, Volume 192, Issue 7, Pages 951–968
DOI: https://doi.org/10.1070/SM2001v192n07ABEH000577 (Mi sm577)

This article is cited in 21 scientific papers (total in 21 papers)

Integrable geodesic flows on homogeneous spaces

A. V. Bolsinov^a, B. Jovanović

^a M. V. Lomonosov Moscow State University

English version PDF (235 kB) Citations (21) Russian version article

References:

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DOI: https://doi.org/10.1070/SM2001v192n07ABEH000577

Abstract: It is proved that the geodesic flow of a bi-invariant metric on an arbitrary homogeneous space of a compact Lie group is Liouville-integrable in the non-commutative sense.

Received: 10.05.2000

Bibliographic databases:

UDC: 513.944

MSC: Primary 37J35, 53D25; Secondary 53C30

Language: English

Original paper language: Russian

Citation: A. V. Bolsinov, B. Jovanović, “Integrable geodesic flows on homogeneous spaces”, Sb. Math., 192:7 (2001), 951–968

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm577

https://doi.org/10.1070/SM2001v192n07ABEH000577

https://www.mathnet.ru/eng/sm/v192/i7/p21

This publication is cited in the following 21 articles:

Dmitri Bykov, Andrew Kuzovchikov, “The classical and quantum particle on a flag manifold”, Class. Quantum Grav., 41:20 (2024), 205009
Bozidar Jovanović, Tijana Šukilović, Srdjan Vukmirović, “Integrable Systems Associated to the Filtrations of Lie Algebras”, Regul. Chaotic Dyn., 28:1 (2023), 44–61
Mykytyuk I.V., “Integrability of Geodesic Flows For Metrics on Suborbits of the Adjoint Orbits of Compact Groups”, Transform. Groups, 21:2 (2016), 531–553
B. Gajić, V. Dragović, B. Jovanović, “On the completeness of the Manakov integrals”, J. Math. Sci., 223:6 (2017), 675–685
Yuri N Fedorov, Božidar Jovanović, “Three natural mechanical systems on Stiefel varieties”, J. Phys. A: Math. Theor, 45:16 (2012), 165204
Fedorov Yu.N., Jovanovic B., “Geodesic Flows and Neumann Systems on Stiefel Varieties: Geometry and Integrability”, Math. Z., 270:3-4 (2012), 659–698
Jovanovic B., “Geodesic Flows on Riemannian g.o. Spaces”, Regular & Chaotic Dynamics, 16:5 (2011), 504–513
Butler L.T., “Positive-entropy integrable systems and the Toda lattice, II”, Mathematical Proceedings of the Cambridge Philosophical Society, 149:3 (2010), 491–538
Jovanovic B., “Integrability of invariant geodesic flows on n-symmetric spaces”, Annals of Global Analysis and Geometry, 38:3 (2010), 305–316
Dragović V., Gajić B., Jovanović B., “Singular Manakov flows and geodesic flows on homogeneous spaces of $\mathrm{SO}(N)$ ”, Transform. Groups, 14:3 (2009), 513–530
Bolsinov A.V., Jovanović B., “Magnetic flows on homogeneous spaces”, Comment. Math. Helv., 83:3 (2008), 679–700
A. A. Magazev, I. V. Shirokov, “Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces”, Russian Math. (Iz. VUZ), 50:8 (2006), 38–49
D. I. Efimov, “The magnetic geodesic flow on a homogeneous symplectic manifold”, Siberian Math. J., 46:1 (2005), 83–93
Butler L.T., “Invariant fibrations of geodesic flows”, Topology, 44:4 (2005), 769–789
Butler L.T., “Manifolds of infinite topological type with integrable geodesic flows”, Manuscripta Math., 116:1 (2005), 99–113
Butler L.T., “Toda lattices and positive-entropy integrable systems”, Invent. Math., 158:3 (2004), 515–549
Mykytyuk I.V., Panasyuk A., “Bi-Poisson structures and integrability of geodesic flow on homogeneous spaces”, Transform. Groups, 9:3 (2004), 289–308
Bolsinov A.V., Jovanović B., “Complete involutive algebras of functions on cotangent bundles of homogeneous spaces”, Math. Z., 246:1-2 (2004), 213–236
Bolsinov A.V., “Integrable geodesic flows on Riemannian manifolds: Construction and obstructions”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 57–103
Bolsinov A.V., Jovanović B., “Noncommutative integrability, moment map and geodesic flows”, Ann. Global Anal. Geom., 23:4 (2003), 305–322

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	796
Russian version PDF:	306
English version PDF:	52
References:	125
First page:	1

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