HAMILTONIANS WITH TWO DEGREES OF FREEDOM ADMITTING A SINGLEVALUED GENERAL SOLUTION

HAMILTONIANS WITH TWO DEGREES OF FREEDOM ADMITTING A SINGLEVALUED GENERAL

SOLUTION

R. Conte;M. Musette;C. Verhoeven

【期刊名称】《分析、理论与应用（英文版）》 【年(卷),期】2005(021)002

【摘要】Following the basic principles stated by Painlevé, we first revisit the process of selecting the admissible time-independent Hamiltonians H = (p12 + p22)/2 + V(q1,q2) whose some integer power qjnj (t) of the general solution is a singlevalued function of the complex time t. In addition to the well known rational Then, by establishing the relevant confluences, we restrict the question of the explicit integration of the perform the explicit integration of the quartie cases, thus proving that the seven rational cases have a meromorphic general solution explicitly given by a genus two hyperelliptic function. 【总页数】13页(188-200)

【关键词】two degree of freedom Hamiltonians;Painlevé test;Painlevé property;Hénon-Heiles Hamiltonian;hyperelliptic 【作者】R. Conte;M. Musette;C. Verhoeven

【作者单位】CEA-Saclay, France;Vrije Universiteit, Belgium;Vrije Universiteit, Belgium 【正文语种】中文