Un indice qui affine l'indice de Poincaré-Lefschetz pour les homéomorphismes de surfaces

Details Un indice qui affine l'indice de Poincaré-Lefschetz pour les homéomorphismes de surfaces Un indice qui affine l'indice de Poincaré-Lefschetz pour les homéomorphismes de surfaces

2005-06-02

arxiv.org/abs/math/0506042v1

Mathematics

Dynamical Systems

44 pages, 16 figures, no racoon

Scientific paper

We study the dynamics of surface homeomorphisms around isolated fixed points whose Poincar\'{e}-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.

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