On the Chebyshev Property of a Class of Hyperelliptic Abelian Integrals

• Yangjian Sun ^[1] ; Shaoqing Wang ^[2] ; Jiazhong Yang ^[3]
  1. [1] Shangrao Normal University

     Shangrao Normal University

     China

     
  2. [2] Central China Normal University

     Central China Normal University

     China

     
  3. [3] Peking University

     Peking University

     China

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01136-3
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• Resumen

  • This paper aims to demonstrate the Chebyshev property of the linear space V = { 2 i=0 αi h x2i ydx : α0, α1, α2 ∈ R, h ∈ } (which is equivalent to that every function of V has at most 2 zeros, counted with multiplicity), with three hyperelliptic Abelian integrals h x2i ydx (i = 0, 1, 2) as generators, where h is an oval determined by H(x, y) = y2 2 + (x) = h, and (x) is an even polynomial of indefinite degree with real non-Morse critical points. As an application, we can obtain the exact upper bound for the number of zeros of a class of hyperelliptic Abelian integrals related to some planar polynomial Hamiltonian systems with two cusps and a nilpotent center.

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