  Within the microscopic transport, systematic investigation of the many facets
of hyperons and hypernuclei up to strangeness $S = -2$ are carried out for
$^{197}$Au + $^{197}$Au and $^{40}$Ca + $^{40}$Ca at the incident energy of
$3A$ GeV. The spatial, temporal and density distributions of hyperon
production, absorption and freeze-out are thoroughly investigated. The rapidity
and kinetic energy spectra of $\Xi$ hyperons and double $\Lambda$ hypernuclei
are analyzed. It is revealed that the chemical balance of hyperon production is
established in baryon-baryon channels while the opposite is found in
baryon-meson channels. It turns out that the rapidity spectra of
$^{4,5}_{\Lambda\Lambda}$X are single-peak and more than two orders of
magnitude lower than that of $^{3}_{\Lambda}$H. Formation of double $\Lambda$
hypernuclei through $\Xi$ hypernuclei as intermediate states is also discussed
in kinematics.
