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Highest weak focus order for trigonometric Liénard equations

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Issue date
2020
Author
Gasull, Armengol
Giné, Jaume
Valls, Claudia
Suggested citation
Gasull, Armengol; Giné, Jaume; Valls, Claudia; . (2020) . Highest weak focus order for trigonometric Liénard equations. Annali di Matematica Pura ed Applicata, 2020, vol.199, p. 1673-1684. https://doi.org/10.1007/s10231-019-00936-8.
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Abstract
Given a planar analytic differential equation with a critical point which is a weak focus of order k, it is well known that at most k limit cycles can bifurcate from it. Moreover, in case of analytic Liénard differential equations this order can be computed as one half of the multiplicity of an associated planar analytic map. By using this approach, we can give an upper bound of the maximum order of the weak focus of pure trigonometric Liénard equations only in terms of the degrees of the involved trigonometric polynomials. Our result extends to this trigonometric Liénard case a similar result known for polynomial Liénard equations.
URI
http://hdl.handle.net/10459.1/71000
DOI
https://doi.org/10.1007/s10231-019-00936-8
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Annali di Matematica Pura ed Applicata, 2020, vol.199, p. 1673-1684
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  • Articles publicats (Matemàtica) [358]
  • Publicacions de projectes de recerca del Plan Nacional [2958]

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