Limit cycles in refracted Hamiltonian systems with a straight switching line

This paper presents a criterion that provides an easy sufficient condition for a collection of line integrals to have the Chebyshev property. The condition is based on the functions appearing in the line integrals. The criterion is used to study the number of limit cycles in refracted differential systems, which are formed by two Hamiltonian differential systems separated by a straight line. The paper concludes by presenting new results on such systems, which show the effectiveness of the criterion presented.