Asymptotically stable dynamical systems are linear

Roger McCann

Vol. 81 (1979), No. 2, 475–479

DOI: 10.2140/pjm.1979.81.475

Abstract

If π is a dynamical system on a locally compact metric space X which has a globally asymptotically stable critical point, then π can be embedded into a dynamical system on l₂ which is derived from a linear differential equation. If X is n-dimensional, then l₂ may be replaced by R²ⁿ.

Mathematical Subject Classification 2000

Primary: 54H20

Milestones

Received: 9 August 1978

Revised: 21 September 1978

Published: 1 April 1979