Title

A Fixed Point Theorem for Bounded Dynamical Systems

Document Type

Article

Publication Date

2002

Department

Mathematics

Language

English

Publication Title

Illinois Journal of Mathematics

Abstract

We show that a continuous map or a continuous flow Rn 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 Rn 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

For more information on the published version, visit Project Euclid's Website.

Also see: " Addendum to: "A Fixed Point Theorem for Bounded Dynamical Systems'' published as:
Richeson, David, and Jim Wiseman. "Addendum to: "A Fixed Point Theorem for Bounded Dynamical Systems''' Illinois Journal of Mathematics 48, no. 3 (2004): 1079-1080. https://www.projecteuclid.org/euclid.ijm/1258131072

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