2005/06/02 by Frédéric Le Roux, Roux, Frédéric Le
Mathematics · #37B30 #37E30 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.math/0506042
openalex publication_date 2005/06/02 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We study the dynamics of surface homeomorphisms around isolated fixed points whose Poincaré-Lefschetz index is not equal to 1. We construct a new conjugacy invariant, which is a cyclic word on the alphabet \\ua, \ra, \da, \la\. 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.