弱焦点的类属开折的刻画
Characterization of the generic unfolding of a weak focus
摘要：
本文给出了一般实解析族对原点具有弱焦点的实解析向量场展开的叶理的几何描述，并证明了两个这类族是轨道解析等价的当且仅当对奇点的复化Poincaré映射展开的复同态族是共轭的.此外，通过沿着一个方便的复横截面的纤维变换，在爆破（拟共形手术）中移动形式正规形的叶子，可以构造一个复维为2的抽象流形，该流形配备有一个椭圆全纯叶理，其单值映射与一个给定的可容许的复同态族相一致。
英文摘要：
In this paper we give a geometric description of the foliation of a generic real analytic family unfolding a real analytic vector field with a weak focus at the origin, and show that two such families are orbitally analytically equivalent if and only if the families of diffeomorphisms unfolding the complexified Poincaré map of the singularities are conjugate. Moreover, by shifting the leaves of the formal normal form in the blow-up (quasiconformal surgery) by means of a fibered transformation along a convenient complex cross-section, one constructs an abstract manifold of complex dimension 2 equipped with an elliptic holomorphic foliation whose monodromy map coincides with a given family of admissible diffeomorphisms.
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