2017
Том 69
№ 7

All Issues

Hamiltonian geometric connection associated with adiabatically perturbed Hamiltonian systems and the existence of adiabatic invariants

Prikarpatskii Ya. A.

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Abstract

Differential-geometric properties of the Hamiltonian connections on symplectic manifolds for the adiabatically perturbed Hamiltonian system are studied. Namely, the associated Hamiltonian connection on the main foliation is constructed and its description is given in terms of covariant derivatives and the curvature form of the corresponding connection.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 3, pp 441-448.

Citation Example: Prikarpatskii Ya. A. Hamiltonian geometric connection associated with adiabatically perturbed Hamiltonian systems and the existence of adiabatic invariants // Ukr. Mat. Zh. - 2008. - 60, № 3. - pp. 382–387.

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