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Published 2015 | Submitted
Book Section - Chapter Open

Spectral curves and discrete Painlevé equations

Abstract

It is well known that isomonodromic deformations admit a Hamiltonian description. These Hamiltonians appear as coefficients of the characteristic equations of their Lax matrices, which define spectral curves for linear systems of differential and difference systems. The characteristic equations in the case of the associated linear problems for various discrete Painlevé equations is biquadratic in the Painlevé variables. We show that the discrete isomonodromic deformations that define the discrete Painlevé equations may be succinctly described in terms of the characteristic equation of their Lax matrices.

Additional Information

© 2015 American Mathematical Society. We would like to acknowledge helpful discussions with Prof. Eric Rains and Prof. Anton Dzhamay, we would like to acknowledge Prof. Basil Grammaticos for alerting us to some relevant literature.

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