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Why do the periodic points of homeomorphisms of the Euclidean plane rotate around certain fixed points? (Pourquoi les points périodiques des homéomorphismes du plan tournent-ils autour decertains points fixes ?) (French) Zbl 1168.37010
Author’s abstract: Let $$f$$ be an orientation-preserving homeomorphism of the euclidean plane $$\mathbb R^2$$ that has a periodic point $$z^*$$ of period $$q \geq 2$$. We prove the existence of a fixed point $$z$$ such that the linking number between $$z^*$$ and $$z$$ is different from zero. That means that the rotation number of $$z^*$$ in the annulus $$\mathbb R^2 \setminus \{z\}$$ is a non-zero element of $$\mathbb R/\mathbb Z$$. This gives a positive answer to a question asked by John Franks.

##### MSC:
 3.7e+100 Low-dimensional dynamical systems
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