This is the hole picture of the r2 = 0 Poincare section.
Click mouse in the window to see a new (red) orbit. Initial coordinates of the
first (blue) electron are shown in the status bar below.
The eZe system is conjectured to be purely hyperbolic (i.e. all orbits are unstable).
This regular motion leads to closed torus structure on the picture below.
The fixed point in the center of the structure is also stable when the
electrons move in a (slightly) off-collinear arrangement. Therefore the
periodic orbit is embedded in an island of stability in the hole phase space.
If the initial distance is smaller then a critical value r1 ~ 5 (while the inner electron is at the nucleus) the first electron is "kicked" out of the atom and ionizes immediately.
 Klaus Richter, Gregor Tanner and Dieter Wintgen
"Classical mechanics of two-electron atoms" Phys.Rev.A 48, 4182 (1993)