Abstract
This chapter analyzes periodic solutions of Hamiltonian systems of ordinary differential equations. The study of the existence of periodic solutions of general Hamiltonian systems has mainly focused on two questions: (1) solutions having a prescribed energy and (2) solutions having a prescribed period. The chapter discusses the fixed energy case. It considers a Hamiltonian system p˙ = −Hq(p, q) and q˙ = Hp(p, q), where “˙” denotes d/dt and Hp, Hq denote the partial derivatives of H with respect to p and q. Setting z = (p, q) the equation is rewritten as z = JHz(z). The chapter highlights and discusses the work done by Seifert and Weinstein in this field.
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