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SIAM J. MUMER. ANAL. (C) 1986 Society for Industrial and Applied Mathemaics Vol. 23, No. 5, October 1986 008. STABLE ATrRACTING SETS IN DYNAMICAL SYSTEMS. AND IN THEIR ONE-STEP DISCRETIZATIONS*. P. E. KLOEDEN-$ AND J. LORENZt Dedicated to Herbert B. Keller on the occasion of his 60th birthday Abstract. We consider a dynamical system described by a system of ordinary differential equations which possesses a compact attracting set A of arbitrary shape. Under the assumption of uniform asymptotic stability of A in the sense of Lyapunov, we show that discretized versions of the dynamical system involving one-step numerical methods have nearby attracting sets A(h), which are also uniformly asymptotically stable. Our proof uses the properties of a Lyapunov function which characterizes the stability of A.

SIAM J. MUMER. ANAL. Vol. 23, No. 5, October 1986 (C) 1986 Society for Industrial andApplied Mathemaics 008 STABLE ATrRACTING SETS IN DYNAMICALSYSTEMS AND IN THEIR ONE-STEP DISCRETIZATIONS*

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