Separation of variables for some systems with a~fourth-order integral of motion
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 3, pp. 468-481
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We construct separation variables for Yehia's integrable deformations of the Kovalevskaya top and the Chaplygin system on a sphere. In the general case, the corresponding quadratures are given by the Abel–Jacobi map on a two-dimensional submanifold of the Jacobian of a genus-three algebraic curve, which is not hyperelliptic.
Keywords:
bi-Hamiltonian geometry, separation of variables, Kovalevskaya top.
@article{TMF_2013_177_3_a3,
author = {Yu. A. Grigor'ev and V. A. Khudobakhshov and A. V. Tsiganov},
title = {Separation of variables for some systems with a~fourth-order integral of motion},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {468--481},
publisher = {mathdoc},
volume = {177},
number = {3},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2013_177_3_a3/}
}
TY - JOUR AU - Yu. A. Grigor'ev AU - V. A. Khudobakhshov AU - A. V. Tsiganov TI - Separation of variables for some systems with a~fourth-order integral of motion JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2013 SP - 468 EP - 481 VL - 177 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2013_177_3_a3/ LA - ru ID - TMF_2013_177_3_a3 ER -
%0 Journal Article %A Yu. A. Grigor'ev %A V. A. Khudobakhshov %A A. V. Tsiganov %T Separation of variables for some systems with a~fourth-order integral of motion %J Teoretičeskaâ i matematičeskaâ fizika %D 2013 %P 468-481 %V 177 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2013_177_3_a3/ %G ru %F TMF_2013_177_3_a3
Yu. A. Grigor'ev; V. A. Khudobakhshov; A. V. Tsiganov. Separation of variables for some systems with a~fourth-order integral of motion. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 3, pp. 468-481. http://geodesic.mathdoc.fr/item/TMF_2013_177_3_a3/