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<p>In this paper, we prove that every orientation-preserving homeomorphism of the plane with the topological shadowing property possesses a fixed point. Furthermore, we establish that a hyperbolic linear isomorphism of a Euclidean space satisfies the topological shadowing property if and only if the origin is either a global attractor or a global repeller.</p>

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A fixed point theorem for plane homeomorphisms with the topological shadowing property

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Gonzalo Cousillas

摘要

In this paper, we prove that every orientation-preserving homeomorphism of the plane with the topological shadowing property possesses a fixed point. Furthermore, we establish that a hyperbolic linear isomorphism of a Euclidean space satisfies the topological shadowing property if and only if the origin is either a global attractor or a global repeller.