论文标题
在限制集的限制集
On limit sets for geodesics of meromorphic connections
论文作者
论文摘要
Riemann表面上的Meromorthic连接起源于与Meromormorthic系数的线性普通微分方程的经典理论密切相关。如与广义的Poincaré-Bendixson定理相关的Abate，Bianchi和Tovena。目前，似乎仍然尚不清楚这种地理素学的某些理论上可能的渐近行为是否真的存在。为了填补空白，我们使用紫红色的仿真连接引起的分支仿射结构，以提供几个示例，这些示例具有无限的许多自我交流和相当特殊的欧米茄限制套件。
Meromorphic connections on Riemann surfaces originate and are closely related to the classical theory of linear ordinary differential equations with meromorphic coefficients. Limiting behaviour of geodesics of such connections has been studied by e.g. Abate, Bianchi and Tovena in relation with generalized Poincaré-Bendixson theorems. At present, it seems still to be unknown whether some of the theoretically possible asymptotic behaviours of such geodesics really exist. In order to fill the gap, we use the branched affine structure induced by a Fuchsian meromorphic connection to present several examples with geodesics having infinitely many self-intersections and quite peculiar omega-limit sets.
