Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam
chain, i. e., a chain of alternate heavy and light masses coupled by anharmonic
forces. For hard interaction potentials, discrete breathers in this model are
known to exist either as ``optic breathers'' with frequencies above the optic
band, or as ``acoustic breathers'' with frequencies in the gap between the
acoustic and the optic band. In this paper, bifurcations between different
types of discrete breathers are found numerically, with the mass ratio m and
the breather frequency omega as bifurcation parameters. We identify a period
tripling bifurcation around optic breathers, which leads to new breather
solutions with frequencies in the gap, and a second local bifurcation around
acoustic breathers. These results provide new breather solutions of the FPU
system which interpolate between the classical acoustic and optic modes. The
two bifurcation lines originate from a particular ``corner'' in parameter space
(omega,m). As parameters lie near this corner, we prove by means of a center
manifold reduction that small amplitude solutions can be described by a
four-dimensional reversible map. This allows us to derive formally a continuum
limit differential equation which characterizes at leading order the
numerically observed bifurcations.Comment: 30 pages, 10 figure