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The center-focus problem and reversibility. (English) Zbl 0994.34020

The reversibility is an interesting concept useful in the qualitative theory of differential equations that implies certain geometric properties. For instance, if an orbit of a reversible vector field meets the fixed-point set at two distinct points then it is necessarily a symmetric periodic orbit.
The paper is concerned with the following problem for a class of two-dimensional systems having a center at the singular point: if a system possesses certain symmetries, what can be said about its reversibility? Sufficient and necessary conditions for the analytic planar system to have a center are given and the reversibility of certain classes of polynomial vector fields is discussed.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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