We analyze the dynamical properties of $sim$1500 very metal-poor (VMP; [Fe/H] $lesssim -2.0$) halo stars, based primarily on medium-resolution spectroscopic data from the HK and Hamburg/ESO surveys. These data, collected over the past thirty years, are supplemented by a number of calibration stars and other small samples, along with astrometric information from $Gaia$ DR2. We apply a clustering algorithm to the 4-D energy-action space of the sample, and identify a set of 38 Dynamically Tagged Groups (DTGs), containing between 5 and 30 member stars. Many of these DTGs can be associated with previously known prominent substructures such as $Gaia$-Sausage/Enceladus (GSE), Sequoia, the Helmi Stream (HStr), and Thamnos. Others are associated with previously identified smaller dynamical groups of stars and streams. We identify 10 new DTGs as well, many of which have strongly retrograde orbits. We also investigate possible connections between our DTGs and $sim$300 individual $r$-process-enhanced (RPE) stars from a recent literature compilation. We find that several of these objects have similar dynamical properties to GSE (5), the HStr (4), Sequoia (1), and Rg5 (1), indicating that their progenitors might have been important sources of RPE stars in the Galaxy. Additionally, a number of our newly identified DTGs are shown to be associated with at least two RPE stars each (DTG-2: 3, DTG-7: 2; DTG-27: 2). Taken as a whole, these results are consistent with ultra-faint and/or dwarf spheroidal galaxies as birth environments in which $r$-process nucleosynthesis took place, and then were disrupted by the Milky Way.
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