Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres

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Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres. / Цыганов, Андрей Владимирович.

In: Nonlinearity, Vol. 35, No. 10, 5357, 06.10.2022, p. 5357-5372.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{2f47b8cf69364be8850664157dbfbbb3,

title = "Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres",

abstract = "Abel{\textquoteright}s quadratures for integrable Hamiltonian systems are defined up to a group law of the corresponding Abelian variety A. If A is isogenous to a direct product of Abelian varieties A ≅ A 1 ×⋯× A k, the group law can be used to construct various Lax matrices on the factors A 1, …, A k. As an example, we discuss two-dimensional reducible Abelian variety A = E + × E −, which is a product of one-dimensional varieties E ± obtained by Euler in his study of the two fixed centres problem, and the Lax matrices on the factors E ± ",

keywords = "14H52, 37J35, 70F07, 70G55, integrable systems, Lax matrices, reducible Abelian varieties",

author = "Цыганов, {Андрей Владимирович}",

note = "Publisher Copyright: {\textcopyright} 2022 IOP Publishing Ltd & London Mathematical Society.",

year = "2022",

month = oct,

day = "6",

doi = "10.1088/1361-6544/ac8a3b",

language = "English",

volume = "35",

pages = "5357--5372",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "IOP Publishing Ltd.",

number = "10",

}

RIS

TY - JOUR

T1 - Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres

AU - Цыганов, Андрей Владимирович

PY - 2022/10/6

Y1 - 2022/10/6

N2 - Abel’s quadratures for integrable Hamiltonian systems are defined up to a group law of the corresponding Abelian variety A. If A is isogenous to a direct product of Abelian varieties A ≅ A 1 ×⋯× A k, the group law can be used to construct various Lax matrices on the factors A 1, …, A k. As an example, we discuss two-dimensional reducible Abelian variety A = E + × E −, which is a product of one-dimensional varieties E ± obtained by Euler in his study of the two fixed centres problem, and the Lax matrices on the factors E ±

AB - Abel’s quadratures for integrable Hamiltonian systems are defined up to a group law of the corresponding Abelian variety A. If A is isogenous to a direct product of Abelian varieties A ≅ A 1 ×⋯× A k, the group law can be used to construct various Lax matrices on the factors A 1, …, A k. As an example, we discuss two-dimensional reducible Abelian variety A = E + × E −, which is a product of one-dimensional varieties E ± obtained by Euler in his study of the two fixed centres problem, and the Lax matrices on the factors E ±

KW - 14H52, 37J35, 70F07, 70G55

KW - integrable systems

KW - Lax matrices

KW - reducible Abelian varieties

UR - http://www.scopus.com/inward/record.url?scp=85139243109&partnerID=8YFLogxK

U2 - 10.1088/1361-6544/ac8a3b

DO - 10.1088/1361-6544/ac8a3b

M3 - Article

VL - 35

SP - 5357

EP - 5372

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 10

M1 - 5357

ER -

ID: 98924991