  The periodic orbits of the strongly chaotic cardioid billiard are studied by
introducing a binary symbolic dynamics. The corresponding partition is mapped
to a topological well-ordered symbol plane. In the symbol plane the pruning
front is obtained from orbits running either into or through the cusp. We show
that all periodic orbits correspond to maxima of the Lagrangian and give a
complete list up to code length 15. The symmetry reduction is done on the level
of the symbol sequences and the periodic orbits are classified using symmetry
lines. We show that there exists an infinite number of families of periodic
orbits accumulating in length and that all other families of geometrically
short periodic orbits eventually get pruned. All these orbits are related to
finite orbits starting and ending in the cusp. We obtain an analytical estimate
of the Kolmogorov-Sinai entropy and find good agreement with the numerically
calculated value and the one obtained by averaging periodic orbits. Furthermore
the statistical properties of periodic orbits are investigated.
