Painleve' property of the He'non-Heiles Hamiltonians
msra(2006)
摘要
Time independent Hamiltonians of the physical type H =
(P_1^2+P_2^2)/2+V(Q_1,Q_2) pass the Painleve' test for only seven potentials
$V$, known as the He'non-Heiles Hamiltonians, each depending on a finite number
of free constants. Proving the Painleve' property was not yet achieved for
generic values of the free constants. We integrate each missing case by
building a birational transformation to some fourth order first degree ordinary
differential equation in the classification (Cosgrove, 2000) of such polynomial
equations which possess the Painleve' property. The properties common to each
Hamiltonian are: (i) the general solution is meromorphic and expressed with
hyperelliptic functions of genus two, (ii) the Hamiltonian is complete (the
addition of any time independent term would ruin the Painleve' property).
更多查看译文
关键词
sep- aration of variables,painleve property,darboux coordinates.,hyperelliptic functions,. — henon-heiles hamiltonian,integrable system,ordinary differential equation
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要