Studies on the Garnier system in two variables
Yusuke Sasano
TL;DR
This paper investigates the Hamiltonian structures and symmetries of the Garnier system in two variables, and introduces a generalization of the Okamoto transformation related to the sixth Painlevé system.
Contribution
It provides new insights into the symmetry and holomorphy properties of the Garnier system and generalizes the Okamoto transformation for the Painlevé VI.
Findings
Analysis of Hamiltonian structures and symmetries
Generalization of Okamoto transformation
Enhanced understanding of Garnier system properties
Abstract
We study some Hamiltonian structures of the Garnier system in two variables from the viewpoints of its symmetry and holomorphy properties. We also give a generalization of {\it Okamoto transformation \it}of the sixth Painlev\'e system.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Nonlinear Waves and Solitons · Advanced Topics in Algebra