Geodesic
Noncanonical time transformations relating finite-dimensional integrable systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 1, pp. 27-53

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider dual Stäckel schemes related to each other by a noncanonical transformation of the time variable. We prove that this duality of different integrable systems arises from the multivaluedness of the Abel mapping. We construct the Lax matrices and the $r$-matrix algebras for some integrable systems on a plane. The integrable deformations of the Kepler problem and the Holt-type systems are considered in detail. 
@article{TMF_1999_120_1_a2,
     author = {A. V. Tsiganov},
     title = {Noncanonical time transformations relating finite-dimensional integrable systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {27--53},
     publisher = {mathdoc},
     volume = {120},
     number = {1},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_120_1_a2/}
}
TY  - JOUR
AU  - A. V. Tsiganov
TI  - Noncanonical time transformations relating finite-dimensional integrable systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1999
SP  - 27
EP  - 53
VL  - 120
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1999_120_1_a2/
LA  - ru
ID  - TMF_1999_120_1_a2
ER  - 
%0 Journal Article
%A A. V. Tsiganov
%T Noncanonical time transformations relating finite-dimensional integrable systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1999
%P 27-53
%V 120
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1999_120_1_a2/
%G ru
%F TMF_1999_120_1_a2
A. V. Tsiganov. Noncanonical time transformations relating finite-dimensional integrable systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 1, pp. 27-53. http://geodesic.mathdoc.fr/item/TMF_1999_120_1_a2/