ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

About Boundedness of the Number of Compact Hypersurfaces of Foliations of Differential Systems


Valentine Yur'yevich Tyshchenko

Grodno state university,
Mathematics and computer science faculty


Real singular foliations defined by Pfaff equations and autonomous systems of equations in total differentials are considered. Basing on the indexes of the lacunas of skew-symmetric tenzor fields, the Ostrogradsky formula and the degree of the map of vector fields criterions of boundedness of the number of compact invariant hypersurfaces of considered foliations have been obtained. The results have been adapted for the case two-dimensional autonomous system of ordinary differential equations. Illustrating examples are given.



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