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Bendixson-Dulac criteria for difference equations. (English) Zbl 0915.39001

For the difference equation \(x_{t+1}=f(x_t)\) in \(\mathbb{R}^n\) with \(t\in\mathbb{N}_0\) conditions are given which exclude the existence of a nontrivial periodic orbit. The conditions are analogous to those of J. Bendixson [Sur les courbes définies par des équations différentielles. Acta Math. 24, 1-88 (1901; JFM 31.0328.03)] and H. Dulac [C. R. Acad. Sci., Paris 204, 1703-1706 (1937; Zbl 0016.40003)] for corresponding differential equations.

MSC:

39A10 Additive difference equations
39A12 Discrete version of topics in analysis
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