On Cartwright-Littlewood fixed point theorem
نویسندگان
چکیده
We prove the following generalization of Cartwright–Littlewood fixed point theorem. Suppose h : R 2 → is an orientation preserving planar homeomorphism, and X acyclic continuum. Let C be a component ∩ ( ) . If there c ∈ such that O + ⊆ or − then also contains Our result generalizes earlier results Ostrovski Boroński, answers Question from Boroński (2017). The proof inspired by short Cartwright Littlewood due to Hamilton (1954).
منابع مشابه
On a Generalization of the Cartwright-littlewood Fixed Point Theorem for Planar Homeomorphisms
We prove a generalization of the fixed point theorem of Cartwright and Littlewood. Namely, suppose h : R → R is an orientation preserving planar homeomorphism, and let C be a continuum such that h−1(C) ∪ C is acyclic. If there is a c ∈ C such that {h−i(c) : i ∈ N} ⊆ C, or {h(c) : i ∈ N} ⊆ C, then C also contains a fixed point of h. Our approach is based on Morton Brown’s short proof of the resu...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2022
ISSN: ['0019-3577', '1872-6100']
DOI: https://doi.org/10.1016/j.indag.2022.02.009