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Contribution à l'étude des solutions périodiques et des centres isochrones des systèmes d'équations différentielles ordinaires plans

Abstract : The global subject of this thesis is the study of periodic solutions of the planar systems of ordinary differential equations. It is divided into two parts.
The first part (which is an already published paper, written in collaboration with A. Raouf Chouikha) is devoted to the search of periodic solutions of "generalized Liénard equation". A theorem is proved which insures the existence of such solutions under appropriate assumptions.
The second part is devoted to the search of isochronous centers of the planar polynomial systems of ordinary differential equations. Using C-algorithm we determine eight new cases. We prove also the efficiency of the normal forms method for such investigations; studying some systems of order 2, 3, 4 and recovering in uniform way some already known results. The intensive use of computer algebra turns to be essential for successful application of the used methods.
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https://tel.archives-ouvertes.fr/tel-00348281
Contributor : Islam Boussaada <>
Submitted on : Saturday, December 20, 2008 - 11:12:26 AM
Last modification on : Tuesday, February 5, 2019 - 11:44:10 AM
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  • HAL Id : tel-00348281, version 2

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Islam Boussaada. Contribution à l'étude des solutions périodiques et des centres isochrones des systèmes d'équations différentielles ordinaires plans. Mathématiques [math]. Université de Rouen, 2008. Français. ⟨tel-00348281v2⟩

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