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The relation between a flow and its discretization. (English) Zbl 0753.34029
The author proves for certain hyperbolic flows of the form \(x'=Ax+g(x)\), \(x\in\mathbb{R}^ n\), that if \(h\) is small enough then the \(h\)-time map and the Euler discretization are uniformly topologically conjugated on each compact set \(K\subset\mathbb{R}^ n\). The main ingredient of the proof is the Hartman-Grobman theorem.
Reviewer: H.Kriete (Bochum)

MSC:
37-XX Dynamical systems and ergodic theory
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References:
[1] FEČKAN M.: Asymptotic behaviour of stable manifolds. Proc. Am. Math. Soc. 111 (1991), 585-593. · Zbl 0727.58029 · doi:10.2307/2048352
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[4] MEDVEĎ M.: Dynamické systémy. Veda, Bratislava, 1988.
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