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Branching of Solutions and Nonexistence of Single-Valued integrals

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

Abstract

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
$$ \begin{array}{*{20}{c}} {\frac{{dp}}{{dt}} = - \frac{{\partial H}}{{\partial q}},} & { \cdot \frac{{dq}}{{dt}} = } \\ \end{array} \frac{{\partial H}}{{\partial p}}. $$

Keywords

Riemann Surface Hamiltonian System Meromorphic Function Variational Equation Toda Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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