Symbolic dynamics and Periodic orbits
Symbolic dynamics for Helium atom
Note, that an orbit passing the (r1 = r2) diagonal
must collide with the nucleus (r1 = 0 or
r2 = 0 lines) before coming back to the diagonal.
Empirically, there exists a one-to-one correspondence between binary symbol
sequences and collinear trajectories. The symbols 0 and 1 are
1 if a trajectory crosses the diagonal
between two collisions with nucleus (r1 = 0 or
r2 = 0);
0 if the trajectory does not cross the diagonal
between two collisions.
Self-retracing periodic orbits
The time reversal symmetric (self-retracing) unstable periodic orbit
with symbolic dynamics 1 is shown below
These are the 01 orbit
the 001 orbit
I'm looking for an up-to-date review of
Hydrogen atom dynamics in high magnetic fields
 P.Cvitanovic et al.
Classical and Quantum
Chaos Chap.24: Helium atom
Previous: Poincare maps
updated 3 Apr 2003