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A note on a generalization of Diliberto’s Theorem for certain differential equations of higher dimension. (English) Zbl 1099.37032
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 S. P. 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.
MSC:
37E99 Low-dimensional dynamical systems
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C30 Manifolds of solutions of ODE (MSC2000)
34D10 Perturbations of ordinary differential equations
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