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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 54 NO.3 / (2002))
Complex Vector Fields Having Orbits with Bounded Geometry
Bruno C. A. Scardua,
Pages. 367-392
Abstract Germs of holomoprhic 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
bounded 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.
Contents 1. Introduction
2. Preliminaries
3. Vector fields with integrable volume function
4. Sub-exponetial growth
5. Orbits having finite total curvature
6. Compact foliations with singularities
Key words singular holomorphic foliation, bounded geometry, holonomy group
Mathmatical Subject Classification 32L30, 58F18