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.
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页码：287 / 296
页数：10
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