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Article

Adamec, Ladislav
A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension. (English). Applications of Mathematics, vol. 50 (2005), issue 2, pp. 93-101
MSC: 34C05, 34C30, 34D10, 37E99 | MR 2125152 | Zbl 1099.37032 | DOI: 10.1007/s10492-005-0006-2
Keywords:
Poincaré mapping; variational equation; moving orthogonal system
Summary:
In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.
References:
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