Linear Estimate for the Number of Zeros of Abelian Integrals

Dmitry Novikov, Sergey Malev

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)689-696
Number of pages8
JournalQualitative Theory of Dynamical Systems
Issue number3
StatePublished - 1 Oct 2017


  • Abelian integrals
  • Infinitesimal Hilbert 16th problem
  • Limit cycles

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics


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