Hilbert Number for a Family of Piecewise Nonautonomous Equations

• J. L. Bravo ^[1] ; M. Fernández ^[1] ; I. Ojeda ^[1]
  1. [1] Universidad de Extremadura

     Universidad de Extremadura

     Badajoz, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
• Idioma: inglés
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• Resumen

  • For family x = (a0 + a1 cost + a2 sin t)|x| + b0 + b1 cost + b2 sin t, we solve three basic problems related with its dynamics. First, we characterize when it has a center (Poincaré center focus problem). Second, we show that each equation has a finite number of limit cycles (finiteness problem), and finally we give a uniform upper bound for the number of limit cycles (Hilbert problem 16).