Degenerate bifurcations of resonant tori in Hamiltonian systems
George Voyatzis and Simos Ichtiaroglou
Department of Physics -
University of Thessaloniki, Greece
The twist condition is a necessary condition in integrable Hamiltonian
systems and symplectic maps to obtain Poincaré-Birkhoff bifurcations under
small perturbations. When this condition does not hold, topological
structures other than Poincaré--Birkhoff chains arise in phase
space through bifurcations of isolated periodic orbits
and reconnections of asymptotic manifolds. In this paper
we construct an integrable model Hamiltonian with degeneracies
suitable to observe these phenomena close to non-twist resonant tori.
The generation of isochronous chains and the stability of their fixed
points is determined analytically and a condition for the reconnection
is found. Particular examples are given, illustrating the bifurcation and
reconnection scenario for several cases of degeneracy.