  We search for dynamical substructures in the LAMOST DR3 very metal-poor (VMP)
star catalog. After cross-matching with Gaia DR2, there are 3300 VMP stars with
available high-quality astrometric information that have halo-like kinematics.
We apply a method based on self-organizing maps to find groups clustered in the
4D space of orbital energy and angular momentum. We identify 57 dynamically
tagged groups, which we label DTG-1 to DTG-57. Most of them belong to existing
substructures in the nearby halo, such as the $Gaia$ Sausage or Sequoia. The
stream identified by Helmi et al. is recovered, but the two disjoint portions
of the substructure have distinct dynamical properties. The very retrograde
substructure Rg5 found previously by Myeong et al. is also retrieved. We report
6 new DTGs with highly retrograde orbits, 2 with very prograde orbits, and 12
with polar orbits. By mapping other datasets (APOGEE halo stars, and catalogs
of r-process-enhanced and CEMP stars) onto the trained neuron map, we can
associate stars with detailed chemical abundances to the DTGs, and look for
associations with chemically peculiar stars. The highly eccentric $Gaia$
Sausage groups contain representatives both of debris from the satellite itself
(which is $\alpha$-poor) and the Splashed Disk, sent up into eccentric halo
orbits from the encounter (and is $\alpha$-rich). The new prograde
substructures also appear to be associated with the Splashed Disk. The DTGs
belonging to the $Gaia$ Sausage host two relatively metal-rich $r$-II stars and
six CEMP stars in different sub-classes, consistent with the idea that the
$Gaia$ Sausage progenitor is a massive dwarf galaxy. Rg5 is dynamically
associated with two highly $r$-process-enhanced stars with [Fe/H] $\sim -$3.
This finding indicates that its progenitor might be an ultra-faint dwarf galaxy
that has experienced $r$-process enrichment from neutron star mergers.

Astrophysics of Galaxies