Analytic-non-integrability of an integrable analytic Hamiltonian system

被引：6
|
作者：
Gorni, G
Zampieri, G
机构：
[1] Univ Udine, Dipartimento Matemat & Informat, I-33100 Udine, UD, Italy
[2] Univ Turin, Dipartimento Matemat, I-10123 Turin, TO, Italy
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2005年 / 22卷 / 03期
关键词：
Liouville integrability; real analytic non-integrability;
D O I：
10.1016/j.difgeo.2005.01.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce the polynomial Hamiltonian H(q(1), q(2), p(1), p(2)) := (q(2)(2) + (q(1)(2) + q(2)(2))(2))p(1) -q(1)q(2)p(2) and we prove that the associated Hamiltonian system is Liouville-C-infinity-integrable, but fails to be real-analytically integrable in any neighbourhood of an equilibrium point. The proof only uses power series expansions, and is elementary. (c) 2005 Elsevier B.V. All rights reserved.
引用
收藏
页码：287 / 296
页数：10
相关论文
共 50 条
  • [41] ON THE LOCAL ANALYTIC INTEGRABILITY AT THE SINGULAR POINT OF A CLASS OF LIENARD ANALYTIC DIFFERENTIAL SYSTEMS
    Llibre, Jaume
    Valls, Claudia
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (01) : 253 - 261
  • [42] Integrability and Pseudo-Linearizable Conditions in a Quasi-Analytic System
    Li, Feng
    Wu, Yusen
    ABSTRACT AND APPLIED ANALYSIS, 2012,
  • [43] Obstructions to the continuation of analytic integrals of Hamiltonian systems under non-Hamiltonian perturbations
    Meletlidou, E
    Voyatzis, G
    Ichtiaroglou, S
    PHYSICS LETTERS A, 2001, 286 (01) : 55 - 60
  • [44] Analytic methods to generate integrable mappings
    Maheswari, C. Uma
    Sahadevan, R.
    PRAMANA-JOURNAL OF PHYSICS, 2015, 85 (05): : 807 - 821
  • [45] Analytic vectors in Locally Integrable Structures
    Barostichi, Rafael F.
    Cordaro, Paulo D.
    Petronilho, Gerson
    GEOMETRIC ANALYSIS OF SEVERAL COMPLEX VARIABLES AND RELATED TOPICS, 2011, 550 : 1 - +
  • [46] NOTES ON ANALYTIC FEYNMAN INTEGRABLE FUNCTIONALS
    YOO, I
    CHANG, KS
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1993, 23 (03) : 1133 - 1142
  • [47] Analytic methods to generate integrable mappings
    C UMA MAHESWARI
    R SAHADEVAN
    Pramana, 2015, 85 : 807 - 821
  • [48] EXTERNAL DISTURBANCE TO NON-INTEGRABLE HAMILTONIAN SYSTEM
    TAKAHASHI, K
    ICHIMURA, A
    HIROOKA, H
    SAITO, N
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1985, 54 (02) : 500 - 515
  • [49] ANALYTIC AND NON-ANALYTIC PROOFS
    PFENNING, F
    LECTURE NOTES IN COMPUTER SCIENCE, 1984, 170 : 394 - 413
  • [50] Analytic integrability inside a family of degenerate centers
    Algaba, Antonio
    Checa, Isabel
    Garcia, Cristobal
    Gine, Jaume
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2016, 31 : 288 - 307
12345