Stellar Dynamical Modeling - Counting Conserved Quantities

Knowing the conserved quantities that a galaxy's stellar orbits conform to is important in helping us understand distribution and structures within galaxy. Isolating integrals of motion resonances are particularly important, non-isolating less so. We compare behavior results two methods for counting number quantities, one based on correlation integral approach other more recent method using machine learning. Both use orbit trajectories phase space as their only input, we create such from theoretical spherical, axisymmetric triaxial model galaxies. The have known isolating resonances. find neither fully effective recovering numbers these nor determining integrals. From computer performance perspective, be faster. Determining algebraic formulae (multiple) has not been possible due lack an appropriate symbolic regression capability. Notwithstanding shortcomings noted, it may usable part trajectory analysis tool kit.