an:05518893
Zbl 1168.37010
Le Calvez, Patrice
Why do the periodic points of homeomorphisms of the Euclidean plane rotate around certain fixed points?
FR
Ann. Sci. ??c. Norm. Sup??r. (4) 41, No. 1, 141-176 (2008).
00233768
2008
j
37E99
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.
Iuliana Oprea (Fort Collins)