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In this paper, we study the existence of limit cycles in continuous anddiscontinuous planar piecewise linear Hamiltonian differential systems with twoor three zones separated by straight lines and such that the linear systemsthat define the piecewise one have isolated singular points, i.e. centers orsaddles. In this case, we show that if the planar piecewise linear Hamiltoniandifferential system is either continuous or discontinuous with two zones, thenit has no limit cycles. Now, if the planar piecewise linear Hamiltoniandifferential system is discontinuous with three zones, then it has at most onelimit cycle, and there are examples with one limit cycle. More precisely,without taking into account the position of the singular points in the zones,we present examples with the unique limit cycle for all possible combinationsof saddles and centers.

Limit Cycles from Planar Piecewise Linear Hamiltonian differential Systems with Two or Three Zones