On a variant of Hilbert's 16th problem

Armengol Gasull; Paulo Henrique Reis Santana

doi:10.1088/1361-6544/ad8c1b

On a variant of Hilbert's 16th problem

Armengol Gasull, Paulo Henrique Reis Santana

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Resum

We study the number of limit cycles that a planar polynomial vector field can have as a function of its number m of monomials. We prove that the number of limit cycles increases at least quadratically with m and we provide good lower bounds for m ≤ 10.

Idioma original	Anglès
Revista	Nonlinearity
Volum	37
Número	12
DOIs	https://doi.org/10.1088/1361-6544/ad8c1b
Estat de la publicació	Publicada - 2024

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10.1088/1361-6544/ad8c1b

https://ddd.uab.cat/record/307723

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https://www.scopus.com/pages/publications/85209406488

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title = "On a variant of Hilbert's 16th problem",

abstract = "We study the number of limit cycles that a planar polynomial vector field can have as a function of its number m of monomials. We prove that the number of limit cycles increases at least quadratically with m and we provide good lower bounds for m ≤ 10.",

keywords = "Limit cycles, Hilbert 16th problem, Abelian integrals",

author = "Armengol Gasull and Santana, \{Paulo Henrique Reis\}",

year = "2024",

doi = "10.1088/1361-6544/ad8c1b",

language = "English",

volume = "37",

journal = "Nonlinearity",

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T1 - On a variant of Hilbert's 16th problem

AU - Gasull, Armengol

AU - Santana, Paulo Henrique Reis

PY - 2024

Y1 - 2024

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AB - We study the number of limit cycles that a planar polynomial vector field can have as a function of its number m of monomials. We prove that the number of limit cycles increases at least quadratically with m and we provide good lower bounds for m ≤ 10.

KW - Limit cycles

KW - Hilbert 16th problem

KW - Abelian integrals

UR - https://www.scopus.com/pages/publications/85209406488

U2 - 10.1088/1361-6544/ad8c1b

DO - 10.1088/1361-6544/ad8c1b

M3 - Article

SN - 0951-7715

VL - 37

JO - Nonlinearity

JF - Nonlinearity

IS - 12

ER -

On a variant of Hilbert's 16th problem

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