论文标题
较高属表面的同位旋转集
Homotopic rotation sets for higher genus surfaces
论文作者
论文摘要
本文指出了针对更高属地面同构的同位旋转的定义，以及证明该定义合理的结果的集合。 We first prove elementary results: we prove that this rotation set is star-shaped, we discuss the realisation of rotation vectors by orbits or periodic orbits and we prove the creation of new rotation vectors for some configurations.Then we use the theory developped by Le Calvez and Tal in [LCT18a] to obtain two deeper results:-- If the homotopical rotation set contains the direction of a closed geodesic which has a自我开采，然后存在旋转马蹄形，因此在许多方向上有无限的周期轨道。-如果同位旋转组包含两个相遇的两个封闭的大地测量学的方向，则在许多方向上存在着无限的周期轨道。
This paper states a definition of homotopic rotation set for higher genus surface homeomorphisms, as well as a collection of results that justify this definition. We first prove elementary results: we prove that this rotation set is star-shaped, we discuss the realisation of rotation vectors by orbits or periodic orbits and we prove the creation of new rotation vectors for some configurations.Then we use the theory developped by Le Calvez and Tal in [LCT18a] to obtain two deeper results:-- If the homotopical rotation set contains the direction of a closed geodesic which has a self-intersection, then there exists a rotational horseshoe and hence infinitely many periodic orbits in many directions.-- If the homotopical rotation set contains the directions of two closed geodesics that meet, there exists infinitely many periodic orbits in many directions.
