Abstract
Let f be an orientation-preserving homeomorphism of the euclidean plane ℝ 2 that has a periodic point z * of period q≥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 ℝ 2 ∖{z} is a non-zero element of ℝ/ℤ. This gives a positive answer to a question asked by John Franks.
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