Transient lifetime spectrum of two charged particles in a Paul trap

The transient properties of laser-cooled two charged particles in a Paul tr ap are studied numerically. We find the existence of characteristic lifetim e of an attractor, which is thought to be an important feature of the trans ient dynamics of the weakly dissipative system. The theoretical analysis sh ows that it is caused by pseudo-periodic orbit which is the residual sign o f periodic orbit of the focus-saddle bifurcation. Study of dissipative coup led standard maps shows that this is a general conclusion for weakly dissip ative system.