Abstract
AbstractFor certain finite groups $$G$$
G
of Bäcklund transformations, we show that a dynamics of $$G$$
G
-invariant configurations of $$n|G|$$
n
|
G
|
Calogero–Painlevé particles is equivalent to a certain $$n$$
n
-particle Calogero–Painlevé system. We also show that the reduction of a dynamics on $$G$$
G
-invariant subset of $$n|G|\times n|G|$$
n
|
G
|
×
n
|
G
|
matrix Painlevé system is equivalent to a certain $$n\times n $$
n
×
n
matrix Painlevé system. The groups $$G$$
G
correspond to folding transformations of Painlevé equations. The proofs are based on Hamiltonian reductions.
Funder
HSE University Basic Research Program
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics