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On the determination of Ziglin monodromy groups. (English) Zbl 0739.58018

The author’s abstract: “The monodromy group of a second-order linear differential equation with rational coefficients is called Ziglin if it preserves a nonconstant rational function. The determination of which monodromy groups are Ziglin is essential in integrability questions for complex analytic Hamiltonian systems. In this paper the problem is solved completely for the Fuchsian case by using the Kovacic algorithm to determine the differential Galois group of that second-order equation and then relating this to the monodromy group. Applications are given to Hamiltonian systems.”.

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
34A30 Linear ordinary differential equations and systems
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
13N05 Modules of differentials
13B10 Morphisms of commutative rings
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