  We study the classical dynamics of the collinear positron-hydrogen scattering
system below the three-body breakup threshold. Observing the chaotic behavior
of scattering time signals, we in- troduce a code system appropriate to a
coarse grained description of the dynamics. And, for the purpose of systematic
analysis of the phase space structure, a surface of section is introduced being
chosen to match the code system. Partition of the surface of section leads us
to a surprising conjec- ture that the topological structure of the phase space
of the system is invariant under exchange of the dynamical variables of proton
with those of positron. It is also found that there is a finite set of
forbidden patterns of symbol sequences. And the shortest periodic orbit is
found to be stable, around which invariant tori form an island of stability in
the chaotic sea. Finally we discuss a possible quantum manifestation of the
classical phase space structure relevant to resonances in scattering cross
sections.
