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Melnikov Functions for a Class of Piecewise Hamiltonian Systems
  
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KeyWord:Piecewise smooth system  Melnikov function  Limit cycle  Bifurcation
Author NameAffiliation
Wenwen Hou Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Shanshan Liu Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
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Abstract:
      This paper is concerned with the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semi-straight lines. By constructing a Poincar\'{e} map, we obtain explicit expressions of the first, second and third order Melnikov functions. In addition, we apply their expressions to give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system.