Elliptic sectors and Euler discretization
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In this work we are interested in the elliptic sector of autonomous differential systems with a degenerate equilibrium point at the origin, and in their Euler discretization. When the linear part of the vector field at the origin has two zero eigenvalues, then the differential system has an elliptic sector, under some conditions. We describe this elliptic sector and we show that the associated Euler discretized system has an elliptic sector converging to that of the continuous system when the step size of the discretization tends to zero.
CitationMohdeb, N., Fruchard, A., & Mehidi, N. (2018). Elliptic sectors and Euler discretization. Electronic Journal of Differential Equations, 2018(183), pp. 1-14.
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