A trial symbolic dynamics of the planar three-body problem

Symbolic dynamics is applied to the planar three-body problem. Symbols are defined on the planar orbit when it experiences a syzygy crossing. If the body i is in the middle at the syzygy crossing and the vectorial area of the triangle made with three bodies changes sign from + to -, number i is given to this event, whereas if the vectorial area changes sign from - to +, number i+3 is given. We examine the case of free-fall three-body problem for the first few digits of symbol sequences, and we examine the case with angular momentum only for the first digit of the symbol sequences. This trial experiments show some new aspects of the planar three-body problem.