Branching of Solutions and Nonexistence of Single-Valued integrals

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 31)


Let M 2n be a symplectic complex analytic manifold (M is covered by coordinate neighborhoods of a set of complex charts with coordinates (p, q) ∈ ℂ2n, and the transition maps from chart to chart are invertible holomorphic canonical transformations). Every complex analytic function H(p, q, t): M2n × ℂ → ℂ defines the complex Hamiltonian system
$$ \begin{array}{*{20}{c}} {\frac{{dp}}{{dt}} = - \frac{{\partial H}}{{\partial q}},} & { \cdot \frac{{dq}}{{dt}} = } \\ \end{array} \frac{{\partial H}}{{\partial p}}. $$


Riemann Surface Hamiltonian System Meromorphic Function Variational Equation Toda Lattice 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  1. 1.Department of MathematicsMoscow State UniversityMoscowRussia

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