Holomorphic Dynamics [electronic resource] : Proceedings of the Second International Colloquium on Dynamical Systems, held in Mexico, July 1986 / edited by Xavier Gomez-Mont, José A. Seade, Alberto Verjovski.

First integrals for singular holomorphic foliations with leaves of bounded volume -- Surgery on complex polynomials -- Dicriticalness of a singular foliation -- Invariant manifolds and a preparation lemma for local holomorphic flows and actions -- Stabilite des V-varietes kahleriennes -- Cyclic resultants of reciprocal polynomials -- Persistent cycles for holomorphic foliations having a meromorphic first integral -- Weakly mixing billiards -- Blow up techniques in the kepler problem -- Algebraic solutions of polynomial differential equations and foliations in dimension two -- The space of siegel leaves of a holomorphic vector field -- Deformations of singular holomorphic foliations on reduced compact ?-analytic spaces -- Product singularities and quotients -- Leafspaces and integrability -- Structural stability of germs of vector fields on surfaces with a simple singularity -- Atiyah sequences and complete closed pseudogroups preserving a local parallelism -- Sur les bouts d'une feuille d'un feuilletage au voisinage d'un point singulier isolé.

The objective of the meeting was to have together leading specialists in the field of Holomorphic Dynamical Systems in order to present their current reseach in the field. The scope was to cover iteration theory of holomorphic mappings (i.e. rational maps), holomorphic differential equations and foliations. Many of the conferences and articles included in the volume contain open problems of current interest. The volume contains only research articles.