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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 [2] IRWIN M. C.: Smooth Dynamical Systems. Academic Press, New York, 1980. · Zbl 0465.58001 [3] HIRSCH M. W., SMALE S.: Differential Equations. Dynamical Systems and Linear Algebra, Academic Press, New York, 1974. · Zbl 0309.34001 [4] MEDVEĎ M.: Dynamické systémy. Veda, Bratislava, 1988.
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