A symmetry reduction technique for higher order Painlevé systems

The symmetry reduction of higher order Painlevé systems is formulated in terms of Dirac procedure. A set of canonical variables that admit Dirac reduction procedure is proposed for Hamiltonian structures governing the ${A^{(1)}_{2M}}$ and ${A^{(1)}_{2M-1}}$ Painlevé systems for $M=2,3,...$.

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