An adaptive high-precision algorithm for continuation of symmetric periodic solutions to Hamiltonian systems is proposed. This algorithm is based on the approach offered by B.B. Kreisman to study the structure of families of symmetric periodic solutions. This algorithm is distinguished by high precision, economy of computer resources, and possibility of parallelization and allows one to follow impact orbits, remaining in physical coordinates. Families of eject periodic solutions of the second kind for the plane Hill problem with some types of symmetry are analyzed on the basis of the adaptive algorithm.

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