Fečkan, Michal The relation between a flow and its discretization. (English) Zbl 0753.34029 Math. Slovaca 42, No. 1, 123-127 (1992). 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) Cited in 4 ReviewsCited in 6 Documents MSC: 37-XX Dynamical systems and ergodic theory Keywords:dynamical systems; hyperbolic flows; Euler discretization; Hartman- Grobman theorem × Cite Format Result Cite Review PDF Full Text: EuDML 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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.