C. Sardón

A Morse-Family Integrator for Hamilton--Jacobi Dynamics Across Caustics

We develop a geometric framework for implicit discrete Hamiltonian systems based on discrete Morse families, Lagrangian relations, and discrete analogues of Tulczyjew's triple. The main idea is to regard the Lagrangian submanifold defining the discrete dynamics, rather than an explicit symplectic evolution map, as the...