Authors: H. Aratyn ; J. F. Gomes ; A. H. Zimerman

We propose a Hamiltonian formalism for $N$ periodic dressing chain with the even number $N$. The formalism is based on Dirac reduction applied to the $N+1$ periodic dressing chain with the odd number $N+1$ for which the Hamiltonian formalism is well known. The Hamilton dressing chain equations in the $N$ even case depend explicitly on a pair of conjugated Dirac constraints and are equivalent to $A^{(1)}_{N-1}$ invariant symmetric Painlevé equations.

Comment: 13 pages, comment added in subsection 3.1

• 37-XX - Dynamical systems and ergodic theory
• 82-XX - Statistical mechanics, structure of matter