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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:
37E99 Low-dimensional dynamical systems
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