# Hamiltonian reductions in Matrix Painlev\'e systems

@inproceedings{Bershtein2022HamiltonianRI, title={Hamiltonian reductions in Matrix Painlev\'e systems}, author={Mikhail Bershtein and Andrei Grigorev and A. Shchechkin}, year={2022} }

For certain ﬁnite groups G of B¨acklund transformations we show that the dynamics of G invariant conﬁgurations of n | G | Calogero–Painlev´e particles is equivalent to certain n -particle Calogero–Painlev´e system. We also show that the reduction of dynamics on G -invariant subset of n | G |× n | G | matrix Painlev´e system is equivalent to certain n × n matrix Painlev´e system. The groups G correspond to folding transformations of Painlev´e equations. The proofs are based on the Hamiltonian…

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