• Corpus ID: 251442572

Hamiltonian reductions in Matrix Painlev\'e systems

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