McCluskey, C. Connell; Muldowney, James S. Bendixson-Dulac criteria for difference equations. (English) Zbl 0915.39001 J. Dyn. Differ. Equations 10, No. 4, 567-575 (1998). 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. Reviewer: Lothar Berg (Rostock) Cited in 20 Documents MSC: 39A10 Additive difference equations 39A12 Discrete version of topics in analysis Keywords:difference equation; periodic orbit Citations:Zbl 0016.40003; JFM 31.0328.03 PDFBibTeX XMLCite \textit{C. C. McCluskey} and \textit{J. S. Muldowney}, J. Dyn. Differ. Equations 10, No. 4, 567--575 (1998; Zbl 0915.39001) Full Text: DOI