A Linear Estimate of the Number of Limit Cycles for A Piecewise Smooth Near-Hamiltonian System

• Chen, Xiaoyan ^[1] ; Han Maoan ^[1]
  1. [1] Zhejiang Normal University

     Zhejiang Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 2, 2020
• Idioma: inglés
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• Resumen

  • In this paper, we study Poincaré bifurcation of limit cycles from a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop round the origin. By using the Melnikov function method, we give an estimation of the number of limit cycles which bifurcate from the period annulus between the center and the homoclinic loop under the piecewise polynomial perturbations of degree n. This result confirms a conjecture.