Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Sublinear discrete-time order-preserving dynamical systems

J. F. Jianga1*

a1 Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China

Abstract

Suppose that the continuous mapping S0305004100074417_inline1 is order-preserving and sublinear. If every positive semi-orbit has compact closure, then every positive semi-orbit converges to a fixed point. This result does not require that the order be strongly preserved.

(Received November 18 1994)

(Revised March 28 1995)

Footnotes

* The research supported by the National Natural Science Foundation of China under grant 19271001.