Codimension two bifurcations of symmetric cycles in Hamiltonian systems with an antisymplectic involution (Q1188336)

A reversible Hamiltonian system depending on parameters \(\mu\) is investigated in a neighbourhood of the origin. It is assumed that the eigenvalues of the linear part are \(\pm ib_ 1,\dots,\pm ib_ n\), nonzero, pure imaginary numbers. The paper describes the typical bifurcations of the families of symmetric cycles at about a dozen different low order resonances \((b_ i/b_ j=\pm1,\pm2\) or \(\pm{1\over 2}\); e.g. \(1,-1,2)\) and indicates the needed number of parameters (here 1 or 2). Proofs are based on methods of bifurcation theory.