Duality for the general isomonodromy problem
Copyright policy )Duality for the general isomonodromy problem
By an extension of Harnad's and Dubrovin's `duality' constructions, the general isomonodromy problem studied by Jimbo, Miwa, and Ueno is equivalent to one in which the linear system of differential equations has a regular singularity at the origin and an irregular singularity at infinity (both resonant). The paper looks at this dual formulation of the problem from two points of view: the symplectic geometry of spaces associated with the loop group of the general linear group, and a generalization of the self-dual Yang-Mills equations.
- University of Oxford United Kingdom
- Mathematical Institute, University of Oxford United Kingdom
Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, Isomonodromic deformations, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Linear ordinary differential equations and systems, FOS: Physical sciences, Symplectic manifolds (general theory), Relations of dynamical systems with symplectic geometry and topology, Yang-Mills and other gauge theories in mechanics of particles and systems, Self-dual Yang-Mills equations, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Riemann-Hilbert problems in context of PDEs, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures, Hamiltonian systems, Exactly Solvable and Integrable Systems (nlin.SI), Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects), Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, Isomonodromic deformations, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Linear ordinary differential equations and systems, FOS: Physical sciences, Symplectic manifolds (general theory), Relations of dynamical systems with symplectic geometry and topology, Yang-Mills and other gauge theories in mechanics of particles and systems, Self-dual Yang-Mills equations, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Riemann-Hilbert problems in context of PDEs, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures, Hamiltonian systems, Exactly Solvable and Integrable Systems (nlin.SI), Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects), Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
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