Complex vector fields having orbits with bounded geometry

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概要

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• Germs of holomorphic vector fields at the origin $0\in C^2$ and polynomial vector fields on $C^2$ are studied. Our aim is to classify these vector fields whose orbits have ounded geometry in a certain sense. Namely, we consider the following situations: (i) the volume of orbits is an integrable function, (ii) the orbits have sub-exponential growth, (iii) the total curvature of orbits is finite. In each case we classify these vector fields under some generic hypothesis on singularities. Applications to questions, concerning polynomial vector fields having closed orbits and complete polynomial vector fields, are given. We also give some applications to the classical theory of compact foliations.

• 東北大学の論文

著者

• Scardua Bruno

  Instituto De Matematica Universidade Federal Do Rio De Janeiro

• Scardua Bruno

  Instituto De Matematica Universidade Federal Do Rio Dejaneiro

関連論文

• A survey of real transverse sections of holomorphic foliations (Complex Dynamics)
• Complex vector fields having orbits with bounded geometry

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