  We study experimentally and theoretically a beam splitter setup for guided
atomic matter waves. The matter wave is a guided atom laser that can be tuned
from quasi-monomode to a regime where many transverse modes are populated, and
propagates in a horizontal dipole beam until it crosses another horizontal beam
at 45$^{\rm o}$. We show that depending on the parameters of this $X$
configuration, the atoms can all end up in one of the two beams (the system
behaves as a perfect guide switch), or be split between the four available
channels (the system behaves as a beam splitter). The splitting regime results
from a chaotic scattering dynamics. The existence of these different regimes
turns out to be robust against small variations of the parameters of the
system. From numerical studies, we also propose a scheme that provides a robust
and controlled beam splitter in two channels only.
