Linear Estimate for the Number of Zeros of Abelian Integrals

• Dmitry Novikov ^[2] ; Sergey Malev ^[1]
  1. [1] University of Edinburgh

     University of Edinburgh

     Reino Unido

     
  2. [2] The Weizmann Institute of Science (Israel)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 3, 2017, págs. 689-696
• Idioma: inglés
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• Resumen

  • 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 x2 y(1 − x − y) = t and ω is a one-form with polynomial coefficients.