Painlevé property and geometry
type: Item
instance of: scholarly article
title: Painlevé property and geometry
zbMATH Open document ID: 0701.58024
DOI: 10.1016/0167-2789(89)90259-5
published in: Physica D
publication date: 1989-01-01T00:00:00Z
review text: It is well known that the Painlevé property for discrete Hamiltonian systems implies the existence of a symplectic manifold which augments the original phase space and on which the flows exist and are analytic for all times. In the paper under review a complete classification of the types of poles allowed in complex time is given for the Hamiltonians which separate into the direct product of hyperelliptic curves. For such systems, bounds on the degrees of the separating variable change, and the other integrals in involution can be found from the pole series. It is also shown how branching can arise naturally in a Painlevé system.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70H20
zbMATH DE Number: 4149192
zbMATH Keywords: discrete Hamiltonian systems
zbMATH Keywords: symplectic manifold
zbMATH Keywords: Painlevé system
author: Nicholas M. Ercolani
author: Eric D. Siggia
reviewed by: Mircea Puta
MaRDI profile type: Publication
full work available at URL: 0167-2789(89)90259-5
OpenAlex ID: W2034007101
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description: scientific article; zbMATH DE number 4149192