A note on a generalization of Diliberto´s theorem for certain differential equations of higher dimension

0025971 - MÚ 2006 RIV CZ eng J - Journal Article
Adamec, Ladislav
A note on a generalization of Diliberto´s theorem for certain differential equations of higher dimension.
[Poznámka o zobecnění Dilibertovy věty pro jisté diferenciální rovnice vyšší dimenze.]
Applications of Mathematics. Roč. 50, č. 2 (2005), s. 93-101. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA ČR(CZ) GA201/99/0295
Institutional research plan: CEZ:AV0Z10190503
Keywords : Poincaré mapping * variational equation * moving orthogonal system
Subject RIV: BA - General Mathematics

It is well known that in the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincare mapping has considerable utility. The use of the Poincare mapping leads to the necessity of calculating its differential and in turn the fundamental matrix of the variational system. For this purpose, a result first obtained by S.P. Diliberto. In the paper this result is extended for a class of autonomous three-dimensional systems of ordinary differential equations admitting a first integral. An apllication of the result obtained is presented.

Práce se pokouší o zobecnění Dilibertovy věty (použité C. Chiconem v řadě prací o rovinných systémech) na n-dimensionální systémy se známými prvními integrály.
Permanent Link: http://hdl.handle.net/11104/0116290