An index which refines the Poincar-Lefschetz index for surface homeomorphisms

• 成果类型: Article
• 署名作者: Le Roux, Frederic
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 1531-1589
• 关键词: fixed-point; translation theorem; plane

摘要

We study the dynamics of surface homeomorphisms around isolated fixed points whose Poincare-Lefschetz index is not equal to 1. We construct a new conjugacy invariant, which is a cyclic word on the alphabet {up arrow, ->, down arrow, <-}. This invariant is a refinement of the P.-L. index. It can be seen as a canonical decomposition of the dynamics into a finite number of sectors of hyperbolic, elliptic or indifferent type. The contribution of each type of sector to the P.-L. index is respectively -1/2, +1/2 and 0. The construction of the invariant implies the existence of some canonical dynamical structures.