## 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 $$index(f^ n,0)=p$$.

### MSC:

 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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### References:

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