Index theorem for homeomorphisms of the plane in the neighborhood of a fixed point
成果类型：
Article
署名作者：
LeCalvez, P; Yoccoz, JC
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
发表日期：
1997
页码：
241-293
关键词：
摘要：
Let f be a local homeomorphism of the plane with a fixed point z which is a locally maximal invariant set and which is neither a sink nor a source. We prove that there are two integers q greater than or equal to 1 and r greater than or equal to 1 such that the sequence i(f(k), z) of the indices at z of the iterates of f satisfy i(f(k), z) = 1 - rq if k is a multiple of q and i(f(k), z) = 1 otherwise. As a corollary we deduce that there is no minimal homeomorphism on the infinite annulus or more generally on the two-dimensional sphere minus a finite set of points. We also construct for a local homeomorphism f as above a topological invariant which is a cyclically ordered set with an automorphism on it; this allows us in particular to define a rotation number for f (rational of denominator q).