# Symbolic dynamics and Periodic orbits

# Symbolic dynamics for Helium atom

Note, that an orbit passing the *(r*_{1} = r_{2}) diagonal
must collide with the nucleus (*r*_{1} = 0 or
*r*_{2} = 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
defined as
*1* if a trajectory crosses the diagonal
between two collisions with nucleus (*r*_{1} = 0 or
*r*_{2} = 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**

[1] *P.Cvitanovic et al.*
Classical and Quantum
Chaos Chap.24: Helium atom

Contents
Previous: Poincare maps

*updated* 3 Apr 2003