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.
引用
收藏
页码：441 / 448
页数：8
相关论文
共 50 条
  • [31] Existence of Homoclinic Orbits of Superquadratic Second-Order Hamiltonian Systems
    Guo, Chengjun
    O'Regan, Donal
    Wang, Chengjiang
    Agarwal, Ravi P.
    ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2015, 34 (01): : 27 - 41
  • [32] On the existence of periodic and homoclinic orbits for first order superquadratic Hamiltonian systems
    Adel Daouas
    Nonlinear Differential Equations and Applications NoDEA, 2013, 20 : 1347 - 1364
  • [33] PERIODIC SOLUTIONS FOR HAMILTONIAN SYSTEMS ASSOCIATED WITH NONLINEAR OSCILLATORS
    Chang, Der-Chen
    Feng, Sheng-Ya
    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2016, 17 (04) : 621 - 637
  • [34] A New Type of Mei Adiabatic Invariant Induced by Perturbation to Mei Symmetry of Hamiltonian Systems
    Ding Ning
    Fang Jian-Hui
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2009, 52 (01) : 12 - 16
  • [35] A New Type of Mei Adiabatic Invariant Induced by Perturbation to Mei Symmetry of Hamiltonian Systems
    DING Ning~(1
    Communications in Theoretical Physics, 2009, 52 (07) : 12 - 16
  • [36] Existence and exponential stability of periodic solutions for a class of Hamiltonian systems on time scales
    Li Yang
    Yongzhi Liao
    Yongkun Li
    Advances in Difference Equations, 2013
  • [37] THE EXISTENCE OF HOMOCLINIC ORBITS FOR A CLASS OF FIRST-ORDER SUPERQUADRATIC HAMILTONIAN SYSTEMS
    Guo, Chengjun
    Agarwal, Ravi P.
    Wang, Chengjiang
    O'Regan, Donal
    MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2014, 61 : 83 - 102
  • [38] Existence and exponential stability of periodic solutions for a class of Hamiltonian systems on time scales
    Yang, Li
    Liao, Yongzhi
    Li, Yongkun
    ADVANCES IN DIFFERENCE EQUATIONS, 2013,
  • [39] Lyapunov–Schmidt Approach to Studying Homoclinic Splitting in Weakly Perturbed Lagrangian and Hamiltonian Systems
    A. M. Samoilenko
    A. K. Prykarpats'kyi
    V. H. Samoilenko
    Ukrainian Mathematical Journal, 2003, 55 (1) : 82 - 92
  • [40] Movable Singularity of Some Hamiltonian Systems Associated with Blowup Phenomena
    Yoshino, Masafumi
    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2024, 60 (03) : 433 - 454
12345