Abstract
Haamiltonian systems of mechanical type are considered on a twisted cotangent stratification of a manifold admitting a smooth free torus action. In the case where these systems possess non-Poisson symmetries generated by the torus action, the Lee-Cartan reduction scheme is described and the structure of a reduced phase space and reduced Hamiltonians is clarified.
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I. O. Parasyuk, “Reduction and coisotropic invariant tori of Hamiltonian systems with non-Poisson commutative symmetries. I,”Ukr. Mat. Zh.,46, No. 5, 537–544 (1994).
S. P. Novikov, “Hamiltonian formalism and a many-valued analog of the Morse theory,”Usp. Mat. Nauk,37, No. 5, 3–49 (1982).
V. I. Arnol'd and A. V. Givental', “Symplectic geometry,” in:VINITI Series in Contemporary Problems of Mathematics [in Russian], Vol. 4, VINITI, Moscow (1985), pp. 4–139.
M. P. Kharlamov, “Reduction of order in mechanical systems with symmetry,”Mekh. Tverd. Tela., Issue 8, 4–18 (1976).
V. I. Arnol'd, V. V. Kozlov, and A. I. Neishtadt, “Mathematical aspects of classical and celestial mechanics,” in:VINITI Series in Contemporary Problems of Mathematics [in Russian], Vol. 3, VINITI, Moscow (1985), pp. 5–304.
S. V. Bolotin, “Comments on the Routh method and the Hertz hypothesis,”Vestn. Mosk. Univ., Ser. Mat., Mekh., No. 5, 51–53 (1986).
I. A. Leonov and M. P. Kharlamov, “Reduction of order in mechanical systems with gyroscopic forces,”Mekh. Tverd. Tela., Issue 17, 35–41 (1985).
V. I. Arnol'd,Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow (1989).
B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko,Modern Geometry [in Russian], Nauka, Moscow (1986).
Sh. Kobayashi and K. Nomizu,Foundations of Differential Geometry [Russian translation], Vol. 1, Nauka, Moscow (1981).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 904–914, July, 1994.
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Parasyuk, I.O. Reduction and coisotropic invariant tori of Hamiltonian systems with non-poisson commutative symmetries. II. Ukr Math J 46, 991–1002 (1994). https://doi.org/10.1007/BF01056676
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DOI: https://doi.org/10.1007/BF01056676