COMPLEX PLANAR HAMILTONIAN SYSTEMS: LINEARIZATION AND DYNAMICS

被引：1
|
作者：
Shi, Hua [1 ]
Zhang, Xiang [1 ,2 ]
Zhang, Yuyan [1 ]
机构：
[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China
[2] Shanghai Jiao Tong Univ, MOE LSC, Shanghai 200240, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2021年 / 41卷 / 07期
关键词：
Complex Hamiltonian system; Liouvillian integrability; linearization; global dynamics; invariant tori; ISOCHRONOUS CENTERS; NORMAL FORMS; INTEGRABILITY;
D O I：
10.3934/dcds.2020406
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Global dynamics of complex planar Hamiltonian polynomial systems is difficult to be characterized. In this paper, for general complex quadratic Hamiltonian systems of one degree of freedom, we obtain some sufficient conditions on the existence of family of invariant tori. We also complete characterization on locally analytic linearizability of complex planar Hamiltonian systems with homogeneous nonlinearity of degrees either 2 or 3 at a nondegenerate singularity, and present their global dynamics. For these classes of systems we also prove existence of families of invariant tori, together with isochronous periodic orbits.
引用
收藏
页码：3295 / 3317
页数：23
相关论文
共 50 条
  • [1] Linearization of Hamiltonian and Gradient Systems
    van der Schaft, A. J.
    [J]. IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 1984, 1 (02) : 185 - 198
  • [2] On the linearization of Hamiltonian systems on Poisson manifolds
    Vorob'ev, YM
    [J]. MATHEMATICAL NOTES, 2005, 78 (3-4) : 297 - 303
  • [3] On the Linearization of Hamiltonian Systems on Poisson Manifolds
    Yu. M. Vorob'ev
    [J]. Mathematical Notes, 2005, 78 : 297 - 303
  • [4] Geometric Linearization for Constraint Hamiltonian Systems
    Paliathanasis, Andronikos
    [J]. SYMMETRY-BASEL, 2024, 16 (08):
  • [5] RG-Whitham dynamics and complex Hamiltonian systems
    Gorsky, A.
    Milekhin, A.
    [J]. NUCLEAR PHYSICS B, 2015, 895 : 33 - 63
  • [6] Linearization of Hamiltonian systems through state immersion
    Menini, Laura
    Tornambe, Antonio
    [J]. 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, : 1261 - 1266
  • [7] Infinitesimal Poisson algebras and linearization of Hamiltonian systems
    J. C. Ruíz-Pantaleón
    D. García-Beltrán
    Yu. Vorobiev
    [J]. Annals of Global Analysis and Geometry, 2020, 58 : 415 - 431
  • [8] Infinitesimal Poisson algebras and linearization of Hamiltonian systems
    Ruiz-Pantaleon, J. C.
    Garcia-Beltran, D.
    Vorobiev, Yu.
    [J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2020, 58 (04) : 415 - 431
  • [9] SYMPLECTIC CONNECTIONS AND THE LINEARIZATION OF HAMILTONIAN-SYSTEMS
    MARSDEN, JE
    RATIU, T
    RAUGEL, G
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1991, 117 : 329 - 380
  • [10] Networks of planar Hamiltonian systems
    Tourigny, David S.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 53 : 263 - 277
12345