Translator Disclaimer
Summer 2002 A fixed point theorem for bounded dynamical systems
David Richeson, Jim Wiseman
Illinois J. Math. 46(2): 491-495 (Summer 2002). DOI: 10.1215/ijm/1258136205

Abstract

We show that a continuous map or a continuous flow on $\mathbb{R}^{n}$ 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 $\mathbb{R}^{n}$ 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.

Citation

Download Citation

David Richeson. Jim Wiseman. "A fixed point theorem for bounded dynamical systems." Illinois J. Math. 46 (2) 491 - 495, Summer 2002. https://doi.org/10.1215/ijm/1258136205

Information

Published: Summer 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1014.54028
MathSciNet: MR1936931
Digital Object Identifier: 10.1215/ijm/1258136205

Subjects:
Primary: 37B30
Secondary: 37B25

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.46 • No. 2 • Summer 2002
Back to Top