Polynomial map factorization of symplectic maps

被引：1
|
作者：
Rangarajan, G [1 ]
机构：
[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India
[2] Indian Inst Sci, Ctr Theoret Studies, Bangalore 560012, Karnataka, India
来源：
INTERNATIONAL JOURNAL OF MODERN PHYSICS C | 2003年 / 14卷 / 06期
关键词：
symplectic integration; polynomial maps; Lie perturbation theory;
D O I：
10.1142/S0129183103004991
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the Hamiltonian system is refactorized using polynomial symplectic maps. This method is analyzed for the three degree of freedom case. Finally, we apply this algorithm to study a large particle storage ring.
引用
收藏
页码：847 / 854
页数：8
相关论文
共 50 条
  • [41] Polynomial approximations of symplectic dynamics and richness of chaos in non-hyperbolic area-preserving maps
    Turaev, D
    NONLINEARITY, 2003, 16 (01) : 123 - 135
  • [42] Nontwist symplectic maps in tokamaks
    Caldas, I. L.
    Viana, R. L.
    Szezech, J. D., Jr.
    Portela, J. S. E.
    Fonseca, J.
    Roberto, M.
    Martins, C. G. L.
    da Silva, E. J.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2012, 17 (05) : 2021 - 2030
  • [43] Symplectic Maps for Diverted Plasmas
    Caldas, Ibere Luiz
    Bartoloni, Bruno F.
    Ciro, David
    Roberson, Geraldo
    Schelin, Adriane B.
    Kroetz, Tiago
    Roberto, Marisa
    Viana, Ricardo Luiz
    Iarosz, Kelly Cristiane
    Batista, Antonio Marcos
    Morrison, Philip J.
    IEEE TRANSACTIONS ON PLASMA SCIENCE, 2018, 46 (07) : 2354 - 2361
  • [44] Multidimensional symplectic separatrix maps
    Treschev, D
    JOURNAL OF NONLINEAR SCIENCE, 2002, 12 (01) : 27 - 58
  • [45] Transport Barriers in Symplectic Maps
    R. L. Viana
    I. L. Caldas
    J. D. Szezech Jr.
    A. M. Batista
    C. V. Abud
    A. B. Schelin
    M. Mugnaine
    M. S. Santos
    B. B. Leal
    B. Bartoloni
    A. C. Mathias
    J. V. Gomes
    P. J. Morrison
    Brazilian Journal of Physics, 2021, 51 : 899 - 909
  • [46] Moment maps on symplectic cones
    de Moraes, SFB
    Tomei, C
    PACIFIC JOURNAL OF MATHEMATICS, 1997, 181 (02) : 357 - 375
  • [47] Symbolic encoding in symplectic maps
    Christiansen, F
    Politi, A
    NONLINEARITY, 1996, 9 (06) : 1623 - 1640
  • [48] Gromov invariants and symplectic maps
    Eleny-Nicoleta Ionel
    Thomas H. Parker
    Mathematische Annalen, 1999, 314 : 127 - 158
  • [49] PERIODIC MAPS IN SYMPLECTIC TOPOLOGY
    GIVENTAL, AB
    FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1989, 23 (04) : 287 - 300
  • [50] Multidimensional Symplectic Separatrix Maps
    D. Treschev
    Journal of Nonlinear Science, 2002, 12 : 27 - 58
12345