Linear Estimate for the Number of Zeros of Abelian Integrals

Dmitry Novikov; Sergey Malev

doi:10.1007/s12346-016-0213-0

Linear Estimate for the Number of Zeros of Abelian Integrals

Dmitry Novikov, Sergey Malev

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We prove a linear in deg ω upper bound on the number of real zeros of the Abelian integral I(t) = ∫ _δ ₍ _t ₎ω, where δ(t) ⊂ R² is the real oval x²y(1 - x- y) = t and ω is a one-form with polynomial coefficients.

Original language	English
Pages (from-to)	689-696
Number of pages	8
Journal	Qualitative Theory of Dynamical Systems
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/s12346-016-0213-0
State	Published - 1 Oct 2017
Externally published	Yes

Keywords

Abelian integrals
Infinitesimal Hilbert 16th problem
Limit cycles

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10.1007/s12346-016-0213-0

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abstract = "We prove a linear in deg ω upper bound on the number of real zeros of the Abelian integral I(t) = ∫ δ ( t )ω, where δ(t) ⊂ R2 is the real oval x2y(1 - x- y) = t and ω is a one-form with polynomial coefficients.",

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AU - Malev, Sergey

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N2 - We prove a linear in deg ω upper bound on the number of real zeros of the Abelian integral I(t) = ∫ δ ( t )ω, where δ(t) ⊂ R2 is the real oval x2y(1 - x- y) = t and ω is a one-form with polynomial coefficients.

AB - We prove a linear in deg ω upper bound on the number of real zeros of the Abelian integral I(t) = ∫ δ ( t )ω, where δ(t) ⊂ R2 is the real oval x2y(1 - x- y) = t and ω is a one-form with polynomial coefficients.

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KW - Infinitesimal Hilbert 16th problem

KW - Limit cycles

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Linear Estimate for the Number of Zeros of Abelian Integrals

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Keywords

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