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 |
URI: | http://hdl.handle.net/2003/40110 http://dx.doi.org/10.17877/DE290R-21987 |
Issue Date: | 2021-02-06 |
Rights link: | https://creativecommons.org/licenses/by/4.0/ |
Appears in Collections: | Fakultät für Mathematik |
Files in This Item:
File | Description | Size | Format | |
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Steinmetz2021_Article_Malmquist-TypeTheoremsForCubic.pdf | 305.42 kB | Adobe PDF | View/Open |
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