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This is a survey on finite-dimensional integrable dynamical systems related to Hamiltonian $G$-actions.
T. Levi-Civita and V. Amaldi, Lezioni di Meccanica Razionale , Volume Secondo, Parte Seconda, Bologna, 1927
1927
Earlier work this paper cites.
V. V. Golubev, Lectures on integration of the equations of motion of a rigid body about a fixed point , Moskva, Gostenhizdat, 1953 (in Russian); English translation: Transl. Philadelphia, PA: Coronet Books, 1953
1953
Earlier work this paper cites.
M. Audin, Spinning tops. A course on integrable systems , Cambridge Studies in Advanced Mathematics 51, Cambridge University Press, 1966
1966
Earlier work this paper cites.
N. N. Nekhoroshev, Action-angle variables and their generalization , Tr. Mosk. Mat. O.-va. 26
1972
Earlier work this paper cites.
J. E. Marsden and A. Weinstein, Reduction of symplectic manifolds with symmetry , Rep. Math. Phys. 5
1974
Earlier work this paper cites.
A. Lichnerowicz, Variété symplectique et dynamique associée à une sous-variété , C. R. Acad. Sci. Paris, Sér. A 280
1975
Earlier work this paper cites.
G. W. Schwarz, Smooth functions invariant under the action of a compact Lie group , Topology 14
1975
Earlier work this paper cites.
S. V. Manakov, Note on the integrability of the Euler equations of n n -dimensional rigid body dynamics , Funkc. Anal. Pril. 10
1976
Earlier work this paper cites.
V. I. Arnold, Mathematical methods of classical mechanics , Springer-Verlag, 1978
1978
Earlier work this paper cites.
A. S. Mishchenko and A. T. Fomenko, Euler equations on finite-dimensional Lie groups , Izv. Akad. Nauk SSSR, Ser. Mat. 42
1978
Earlier work this paper cites.
A. S. Mishchenko and A. T. Fomenko, Generalized Liouville method of integration of Hamiltonian systems , Funkts. Anal. Prilozh. 12
1978
Earlier work this paper cites.
V. V. Kozlov and N. N. Kolesnikov, On theorems of dynamics , Prikl. Mat. Mekh. 42
1979
Earlier work this paper cites.
M. Kramer, Spharische untrgruppen in kompakten zusammenhangenden Liegruppen , Compositio Math. 38
1979
Earlier work this paper cites.
J. J. Duistermaat, On global action-angle variables , Comm. Pure Appl. Math. 33
1980
Earlier work this paper cites.
A. S. Mishchenko and A. T. Fomenko, Integration of Hamiltonian systems with noncommutative symmetries , Tr. Semin. Vekt. Tenz. Anal. Prilozh. Geom. Mekh. Fiz. 20
1981
Earlier work this paper cites.
A. Thimm, Integrable geodesic flows on homogeneous spaces , Ergod. Th. Dynam. Sys. 1
1981
Earlier work this paper cites.
S. Benenti and W. M. Tulczyjew, Remarques sur les réductions symplectiques , C. R. Acad. Sci. Paris, 294
1982
Earlier work this paper cites.
J. H. Eschenburg, New examples of manifolds with strictly positive curvature , Invent. Math. 66
1982
Earlier work this paper cites.
A. S. Mishchenko, Integration of geodesic flows on symmetric spaces , Mat. Zametki 31
1982
Earlier work this paper cites.
A. V. Brailov, Complete integrability of some geodesic flows and integrable systems with non-commuting integrals , Dokl. Akad. Nauk SSSR 271
1983
Earlier work this paper cites.
A. V. Brailov, Some cases of complete integrability of the Euler equations and applications , Dokl. Akad. Nauk SSSR 268
1983
Earlier work this paper cites.
V. Guillemin and S. Sternberg, On collective complete integrability according to the method of Thimm , Ergod. Th. Dynam. Sys. 3
1983
Earlier work this paper cites.
I. V. Mikityuk, Homogeneous spaces with integrable G G -invariant Hamiltonian flows , Izv. Akad. Nauk SSSR, Ser. Mat. 47
1983
Earlier work this paper cites.
A. Weinstein, The local tructure of Poisson manifolds , J. Diff. Geom. 18
1983
Earlier work this paper cites.
V. Guillemin and S. Sternberg, Multiplicity-free spaces , J. Diff. Geom. 19
1984
Earlier work this paper cites.
V. Guillemin and S. Sternberg, Symplectic Techniques in Physics , Cambrige University press, 1984
1984
Earlier work this paper cites.
A. V. Brailov, Construction of complete integrable geodesic flows on compact symmetric spaces , Izv. Acad. Nauk SSSR, Ser. Mat. 50
1986
Cited alongside, same era.
P. Dazord and T. Delzant, La probleme general des variables actions-angles , J. Diff. Geom. 26
1987
Cited alongside, same era.
P. Libermann and C. M. Marle, Symplectic geometry and analytic mechanics , Math. Appl. 35
1987
Cited alongside, same era.
I. V. Mikityuk, On the integrability of invariant Hamiltonian systems with homogeneous configuration spaces , Mat. Sbornik 129[171](4)
1987
Cited alongside, same era.
V. I. Arnol’d, V. V. Kozlov and A. I. Neishtadt, Mathematical aspects of classical and celestial mechanics , Itogi Nauki i Tekhniki. Sovr. Probl. Mat. Fundamental’nye Napravleniya , Vol. 3, VINITI, Moscow 1985. English transl.: Encyclopadia of Math. Sciences, Vol.3, Springer-Verlag, Berlin 1989
V. Dragović and B. Gajić, An L-A pair for the Hess–Appel’rot system and a new integrable case for the Euler-Poisson equations on so ( 4 ) × so ( 4 ) \operatorname{so}(4)\times\operatorname{so}(4) , Proc. Roy. Soc. Edinburgh Sect. A 131
2001
Later among the works it cites.
I. V. Mykytyuk, Actions of Borel subgroups on homogeneous spaces of reductive complex Lie groups and integrability , Composito Math. 127
2001
Later among the works it cites.
E. B. Vinberg, Commutative homogeneous spaces and co-isotropic symplectic actions , Uspekhi Mat. Nauk 56
2001
Later among the works it cites.
E. A. Buldaeva, On integrable geodesic flows on the adjoint orbits of orthogonal groups , Diploma work, Dept. of Mathematics and Mechanics, Moscow State University, May 2002
2002
Later among the works it cites.
G. Gaeta, The Poincare-Lyapounov-Nekhoroshev theorem , Ann. Phys. 297
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1989
Cited alongside, same era.
A. A. Oshemkov, On the topological structure of the set of singularities of integrable Hamiltonian systems , In: Topological classification of integrable systems , Adv. in Soviet Math. 6
1991
Cited alongside, same era.
A. V. Bolsinov, Compatible Poisson brackets on Lie algebras and the completeness of families of functions in involution , Izv. Acad. Nauk SSSR, Ser. matem. 55
1992
Cited alongside, same era.
D. I. Panyushev, Complexity of quasiaffine homogeneous varieties, t-decompositions, and affine homogeneous spaces of complexity 1 1 , Adv. in Soviet Math. 8
1992
Cited alongside, same era.
A. L. Onishchik, E. B. Vinberg and V. V. Gorbatsevich, Foundations of Lie Theory and Lie Transformation Groups , Springer-Verlag, 1993
1993
Cited alongside, same era.
N. N. Nekhoroshev, The Poincare–Lyapounov–Liouville–Arnold theorem , Funct. Anal. Appl. 28 (1994), 128–129
1994
Cited alongside, same era.
G. P. Paternain and R. J. Spatzier, New examples of manifolds with completely integrable geodesic flows , Adv. in Math. 108
1994
Cited alongside, same era.
A. G. Reyman and M. A. Semenov-Tian-Shanski, Group theoretical methods in the theory of finite dimensional integrable systems , In: V. I. Arnold, S. P. Novikov (eds.), Dynamical Systems VII , Springer-Verlag 1994, pp. 116–225
1994
Cited alongside, same era.
2002
Later among the works it cites.
B. Jovanović, On the Integrability of Geodesic Flows of Submersion Metrics , Lett. Math. Phys. 61
2002
Later among the works it cites.
A. V. Bolsinov and B. Jovanović, Non-commutative integrability, moment map and geodesic flows , Annals of Global Analysis and Geometry 23
2003
Later among the works it cites.
A. V. Borisov and I. S. Mamaev, The Hess case in the dynamics of a rigid body , Prikl. Mat. Mekh. 67
2003
Later among the works it cites.
A. V. Bolsinov and B. Jovanović, Complete involutive algebras of functions on cotangent bundles of homogeneous spaces , Mathematische Zeitschrift 246
2004
Later among the works it cites.
L. Butler, The Toda Lattice and Positive-Entropy Integrable Systems , Invent. Math. 158
2004
Later among the works it cites.
D. I. Efimov, The magnetic geodesic flows in a homogeneous field on the complex projective space , Siberian Math. J. 45
2004
Later among the works it cites.
Yu. N. Fedorov and B. Jovanović, Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces , J. Non. Sci. 14
2004
Later among the works it cites.
I. V. Mykytyuk and A. Panasyuk, Bi-Poisson structures and integrability of geodesic flows on homogeneous spaces , Transformation Groups 9
2004
Later among the works it cites.
J. P. Ortega and T. S. Ratiu, Momentum Maps and Hamiltonian Reduction , Progress in Math. 222, Birkhäuser, 2004
2004
Later among the works it cites.
A. Panasyuk, Projection of Jordan bi-Poisson structures that are Kronecker, diagonal actions and the classical Gaudin systems , J. Geom. Phys. 47
2004
Later among the works it cites.
S. T. Sadetov, A proof of the Mishchenko–Fomenko conjecture ( 1981 ) (1981) , Dokl. Akad. Nauk 397
2004
Later among the works it cites.
D. I. Efimov, The magnetic geodesic flows on a homogeneous symplectic manifold , Siberian Math. J. 46
2005
Later among the works it cites.
V. V. Kozlov, Remarks on a Lie theorem on the integrability of differential equations in closed form , Diff. Uravn. 41
2005
Later among the works it cites.
N. N. Nekhoroshev, Types of integrability on a submanifold and generalizations of Gordon’s theorem , Tr. Mosk. Mat. Obs. 66
2005
Later among the works it cites.
A. V. Bolsinov and B. Jovanović, Magnetic Geodesic Flows on Coadjoint Orbits , J. Phys. A: Math. Gen. 39
2006
Later among the works it cites.
V. Dragović and B. Gajić, Systems of Hess–Appel’rot type , Comm. Math. Phys. 256
2006
Later among the works it cites.
E. Fiorani and G. Sardanashvily, Noncommutative integrability on noncompact invariant manifolds , J. Phys. A 39
2006
Later among the works it cites.
N. T. Zung, Torus actions and integrable systems , In: A. V. Bolsinov, A. T. Fomenko, A. A. Oshemkov (eds.), Topological Methods in the Theory of Integrable Systems , Cambridge Scientific Publ., 2006; arXive: math.DS/0407455
2006
Later among the works it cites.
B. Jovanović, Partial Reduction of Hamiltonian Flows and Hess–Appelrot Systems on SO ( n ) \operatorname{SO}(n) , Nonlinearity 20
2007
Later among the works it cites.
A. V. Bolsinov and B. Jovanović, Magnetic Flows on Homogeneous Spaces , Com. Mat. Helv., 83
2008
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