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A dynamical property of homeomorphisms of the plane in the neighborhood of a fixed point of index \(>1\). (Une propriété dynamique des homéomorphismes du plan au voisinage d’un point fixe d’indice \(>1\).) (French) Zbl 0976.54046

Summary: We prove that every orientation preserving homeomorphism \(f\) of the plane defined locally around an isolated fixed point of Lefschetz index strictly larger than 1 has a positively or negatively wandering domain in this neighbourhood. Such a situation cannot occur when \(f\) is area preserving and the index must be smaller than or equal to 1.

MSC:

54H20 Topological dynamics (MSC2010)
55M25 Degree, winding number
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