Characterization of the Existence of Non-trivial Limit Cycles for Generalized Abel Equations

• Álvarez, M.J. ^[1] ; Bravo, J.L. ^[2] ; Fernández, M. ^[2] ; Prohens, R. ^[1]
  1. [1] Universitat de les Illes Balears

     Universitat de les Illes Balears

     Palma de Mallorca, España

     
  2. [2] Universidad de Extremadura

     Universidad de Extremadura

     Badajoz, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 1, 2021
• Idioma: inglés
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• Resumen

  • In this paper, we consider the family of generalized Abel equations of the form x = A(t)xm + B(t)xn, where A, B are trigonometric polynomials and m, n ∈ N. We characterize the existence of non-trivial limit cycles in this family, in terms of the trigonometric monomials.