On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields
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It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytic vector fields. In the polynomial case, it is known only that limit cycles of even degree are structurally unstable. In this paper, we prove that non-hyperbolic limit cycles of odd degree are also structurally unstable in the polynomial case, if we consider Whitney’s topology.
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Limit cycles, Polynomial vector fields, Structural stability
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Inglês
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Sao Paulo Journal of Mathematical Sciences, v. 18, n. 2, p. 1605-1618, 2024.
