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 |
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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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