In this paper we study the maximum number of limit cycles of the discontinuous piecewise differential systems with two zones separated by the straight line \(y=0\), in \(y\ge 0\) there is a polynomial Hamiltonian system of degree m, and in \(y\le 0\) there is a polynomial Hamiltonian system of degree n. First for this class of discontinuous piecewise polynomial Hamiltonian systems, which are perturbation of a linear center, we provide a sharp upper bound for the maximum number of the limit cycles that can bifurcate from the periodic orbits of the linear center using the averaging theory up to any order. After for the general discontinuous piecewise polynomial Hamiltonian systems we also give an upper bound for their maximum number of limit cycles in function of m and n. Moreover, this upper bound is reached for some degrees of m and n.

在本文中，我们研究了由直线\（y = 0 \）隔开的两个区域的不连续分段微分系统的极限环的最大数目，在\（y \ ge 0 \）中存在一个多项式哈密顿度系统m，并且在\（y \ le 0 \）中，存在一个次数为n的多项式哈密顿系统。首先，针对这类不连续的分段多项式哈密顿系统，它们是线性中心的摄动，我们提供了最大极限环的上限，该极限环可以使用平均理论从线性中心的周期轨道分叉到任何命令。对于一般的不连续分段多项式哈密顿系统，我们还给出了它们的最大极限环数的上限，该上限是m和n的函数。此外，在一定程度上达到了m和n的上限。