Entanglement in quantum catastrophes

We classify entanglement singularities for various two-mode bosonic systems in terms of catastrophe theory. Employing an abstract phase-space representation, we obtain exact results in limiting cases for the entropy in cusp, butterfly, and two-dimensional catastrophes. We furthermore use numerical results to extract the scaling of the entropy with the non-linearity parameter, and discuss the role of mixing entropies in more complex systems.