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- W2134148934 abstract "We prove a generalization of the fixed point theorem of Cartwright and Littlewood. Namely, suppose $h : mathbb{R}^2 tomathbb{R}^2$ is an orientation preserving planar homeomorphism, and let $C$ be a continuum such that $h^{-1}(C)cup C$ is acyclic. If there is a $cin C$ such that ${h^{-i}(c):iinmathbb{N}}subseteq C$, or ${h^i(c):iinmathbb{N}}subseteq C$, then $C$ also contains a fixed point of $h$. Our approach is based on Morton Brown's short proof of the result of Cartwright and Littlewood. In addition, making use of a linked periodic orbits theorem of Bonino we also prove a counterpart of the aforementioned result for orientation reversing homeomorphisms, that guarantees a $2$-periodic orbit in $C$ if it contains a $k$-periodic orbit ($k>1$)." @default.
- W2134148934 created "2016-06-24" @default.
- W2134148934 creator A5005027748 @default.
- W2134148934 date "2015-10-22" @default.
- W2134148934 modified "2023-09-27" @default.
- W2134148934 title "On a generalization of the Cartwright-Littlewood fixed point theorem for planar homeomorphisms" @default.
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