Electron. J. Differential Equations, Vol. 2018 (2018), No. 183, pp. 1-14.

Elliptic sectors and Euler discretization

Nadia Mohdeb, Augustin Fruchard, Noureddine Mehidi

Abstract:
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.

Submitted September 1, 2018. Published November 14, 2018.
Math Subject Classifications: 34C25, 34C37, 34A34, 39A05.
Key Words: Elliptic sector; nonhyperbolic equilibrium point; homoclinic orbit; S-invertible; Euler discretization.

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Nadia Mohdeb
Laboratoire de Mathématiques Appliquées
Université A. Mira
Bejaia, Algérie
email: n_mohdeb@hotmail.com
Augustin Fruchard
Laboratoire de Mathématiques, Informatique et Applications
Université de Haute Alsace
Mulhouse, France
email: augustin.fruchard@uha.fr
  Noureddine Mehidi
Laboratoire de Mathématiques Appliquées
Université A. Mira
Bejaia, Algérie
email: manogha@yahoo.fr

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