Creation of twistless circles in a model of stellar pulsations

In the present paper, we study the Poincaré 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 Hénon 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 Poincaré map.