  In the present paper, we study the Poincare map associated to a periodic
perturbation, both in space and time, of a linear Hamiltonian system. The
dynamical system embodies the essential physics of stellar pulsations and
provides a global and qualitative explanation of the chaotic oscillations
observed in some stars. We show that this map is an area preserving one with an
oscillating rotation number function. The nonmonotonic property of the rotation
number function induced by the triplication of the elliptic fixed point is
superposed on the nonmonotonic character due to the oscillating perturbation.
This superposition leads to the co-manifestation of generic phenomena such as
reconnection and meandering, with the nongeneric scenario of creation of
vortices. The nonmonotonic property due to the triplication bifurcation is
shown to be different from that exhibited by the cubic Henon map, which can be
considered as the prototype of area preserving maps which undergo a
triplication followed by the twistless bifurcation. Our study exploits the
reversibility property of the initial system, which induces the time-reversal
symmetry of the Poincare map.
