Malmquist-type theorems for cubic Hamiltonians

Steinmetz, Norbert

Malmquist-type theorems for cubic Hamiltonians

dc.contributor.author	Steinmetz, Norbert
dc.date.accessioned	2021-03-26T08:08:39Z
dc.date.available	2021-03-26T08:08:39Z
dc.date.issued	2021-02-06
dc.description.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.	en
dc.identifier.uri	http://hdl.handle.net/2003/40110
dc.identifier.uri	http://dx.doi.org/10.17877/DE290R-21987
dc.language.iso	en	de
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/
dc.subject	Hamiltonian system	en
dc.subject	Painlevé differential equation	en
dc.subject	Painlevé property	en
dc.subject	Malmquist property	en
dc.subject	Algebroid function	en
dc.subject.ddc	520
dc.title	Malmquist-type theorems for cubic Hamiltonians	en
dc.type	Text	de
dc.type.publicationtype	article	de
dcterms.accessRights	open access
eldorado.secondarypublication	true	de
eldorado.secondarypublication.primarycitation	Steinmetz, N. Malmquist-Type Theorems for Cubic Hamiltonians. Comput. Methods Funct. Theory (2021).	de
eldorado.secondarypublication.primaryidentifier	https://doi.org/10.1007/s40315-020-00356-3	de

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