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A fixed point theorem for bounded dynamical systems

David Richeson·Jim Wiseman
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Abstract

We show that a continuous map or a continuous flow on $\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\R^{n}$ intersects W then there is a fixed point in W. Consequently, if the omega limit set of every point is nonempty and uniformly bounded then there is a fixed point.

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David Richeson, Jim Wiseman. 2002-09-23. A fixed point theorem for bounded dynamical systems. https://arxiv.org/abs/math/0108064

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