HAMILTONIAN GEOMETRIC CONNECTION ASSOCIATED WITH ADIABATICALLY PERTURBED HAMILTONIAN SYSTEMS AND THE EXISTENCE OF ADIABATIC INVARIANTS

被引：0
|
作者：
Prykarpats'kyi, Ya. A. [1 ,2 ]
机构：
[1] Ukrainian Natl Acad Sci, Inst Math, Kiev, Ukraine
[2] Krakow Pedag Univ, Krakow, Poland
来源：
UKRAINIAN MATHEMATICAL JOURNAL | 2008年 / 60卷 / 03期
关键词：
Hamiltonian System; Covariant Derivative; Symplectic Manifold; Holonomy Group; Parallel Translation;
D O I：
10.1007/s11253-008-0066-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the differential-geometric properties of Hamiltonian connections on symplectic manifolds for adiabatically perturbed Hamiltonian systems. In particular, an associated Hamiltonian connection is constructed on the principal fibration. Its description is given in terms of covariant derivatives and the curvature form of the corresponding connection.
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页码：441 / 448
页数：8
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