  An analytic reversible Hamiltonian system with two degrees of freedom is
studied in a neighborhood of its symmetric heteroclinic connection made up of a
symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in
the same level of a Hamiltonian and two non-symmetric heteroclinic orbits
permuted by the involution. This is a codimension one structure and therefore
it can be met generally in one-parameter families of reversible Hamiltonian
systems. There exist two possible types of such connections in dependence on
how the involution acts near the equilibrium. We prove a series of theorems
which show a chaotic behavior of the system and those in its unfoldings, in
particular, the existence of countable sets of transverse homoclinic orbits to
the saddle periodic orbit in the critical level, transverse heteroclinic
connections involving a pair of saddle periodic orbits, families of elliptic
periodic orbits, homoclinic tangencies, families of homoclinic orbits to
saddle-centers in the unfolding, etc. As a byproduct, we get a criterion of the
existence of homoclinic orbits to a saddle-center.
