Persistence of homoclinic orbits after discretization of a two dimensional degenerate differential system
Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1503-1510
https://doi.org/10.4134/BKMS.2014.51.5.1503
Printed September 30, 2014
Noureddine Mehidi and Nadia Mohdeb
Laboratoire de Math\'{e}matiques Appliqu\'{e}es, Laboratoire de Math\'{e}matiques Appliqu\'{e}es
Abstract : The aim of this work is to construct a general family of two dimensional differential systems which admits homoclinic solutions near a non-hyperbolic fixed point, such that a Jacobian matrix at this point is zero. We then discretize it by using Euler's method and look after the persistence of the homoclinic solutions in the obtained discrete system.
Keywords : homoclinic orbits, degenerate system, non-hyperbolic fixed point, discrete system
MSC numbers : 34C37, 34A34, 39A05
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