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Monodromy and nonintegrability in complex Hamiltonian systems |
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| Authors: | Alberto Baider Richard C. Churchill David L. Rod |
| Affiliation: | (1) Department of Mathematics, Hunter College, 695 Park Avenue, 10021 New York, New York;(2) Department of Mathematics and Statistics, University of Calgary, T2N 1N4 Calgary, Alberta, Canada |
| Abstract: | This paper investigates the monodromy representation of the normal variational equation along a phase curve of a two-dimensional complex analytic Hamiltonian system. Geometrical conditions are presented which guarantee reducibility, together with additional hypotheses to ensure complete reducibility. Symmetries in the equations are treated in detail. Applications to establishing the nonintegrability of specific systems are presented. |
| Keywords: | (complex) Hamiltonian system (complex) symplectic manifold (non-)integrability two degrees of freedom reduction monodromy representation (normal) variational equation Ziglin theory |
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