On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields

Santana, Paulo

doi:10.1007/s40863-024-00431-w

São Paulo J. Math. Sci.

2024

DOI: 10.1007/s40863-024-00431-w

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On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields

Paulo Santana

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A note on Hilbert 16th problem

Gasull,

Santana

2024

Proc. Amer. Math. Soc.

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Let H ( n ) \mathcal {H}(n) be the maximum number of limit cycles that a planar polynomial vector field of degree n n can have. In this paper we prove that H ( n ) \mathcal {H}(n) is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite.

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A note on Hilbert 16th problem

Gasull,

Santana

2024

Proc. Amer. Math. Soc.

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On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields

Cited by 1 publication

References 38 publications

A note on Hilbert 16th problem

A note on Hilbert 16th problem

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