Hamiltonian Monodromy in a Tavis-Cummings system with an $A_2$ singularity

Our recent preprint Hamiltonian Monodromy in a Tavis-Cummings System with an $A_2$ Singularity, with Gabriela Gutierrez-Guillen, Pavao Mardešić, and Dominique Sugny, analyzes the topology of the singular Lagrangian fibration of the classical two-spin Tavis–Cummings system. We show that this three-degree-of-freedom integrable Hamiltonian system has a singularity of $A_2$ type which has not been previously observed in “well-behaved” singular Lagrangian fibrations and goes beyond the familiar focus–focus ($A_1$) singularity.