On the fixed point index of iterates of planar homeomorphisms. (English) Zbl 0686.58028

Summary: If f is an orientation preserving homeomorphism of the plane with an isolated fixed point at the origin 0 and \(index(f,0)=p\), then \(index(f^ n,0)\) is always well defined provided that \(p\neq 1\). In this case, for each \(n\neq 0\), \(index(f^ n,0)=index(f,0)=p\). If \(index(f,0)=1\), then there is an integer p (possibly \(p=1)\) such that for those values of n for which \(index(f^ n,0)\) is defined (i.e. 0 is an isolated fixed point of \(f^ n)\), \(index(f^ n,0)=1\) or \(index(f^ n,0)=p\).


37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
54H25 Fixed-point and coincidence theorems (topological aspects)
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