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arXiv:math/0108064 [math.DS]AbstractReferencesReviewsResources

A fixed point theorem for bounded dynamical systems

David Richeson, Jim Wiseman

Published 2001-08-08, updated 2002-09-23Version 2

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.

Comments: 4 pages, minor clarifications
Categories: math.DS
Subjects: 54H25, 37B30, 37B25
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