Authors: Steinmetz, Norbert
Title: Malmquist-type theorems for cubic Hamiltonians
Language (ISO): en
Abstract: The aim of this paper is to classify the cubic polynomials H(z,x,y)=∑j+k≤3ajk(z)xjyk over the field of algebraic functions such that the corresponding Hamiltonian system x′=Hy, y′=−Hx has at least one transcendental algebroid solution. Ignoring trivial subcases, the investigations essentially lead to several non-trivial Hamiltonians which are closely related to Painlevé’s equations PI, PII, P34, and PIV . Up to normalisation of the leading coefficients, common Hamiltonians are HI:HII/34:HIV:−2y3+12x2−zyx2y−12y2+12zy+κxx2y+xy2+2zxy+2κx+2λy13(x3+y3)+zxy+κx+λy, but the zoo of non-equivalent Hamiltonians turns out to be much larger.
Subject Headings: Hamiltonian system
Painlevé differential equation
Painlevé property
Malmquist property
Algebroid function
Issue Date: 2021-02-06
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Appears in Collections:Fakultät für Mathematik

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