Hamiltonian rays
``The ocean is opaque to light but transparent to sound'' appears in countless notes, lectures and papers on ocean acoustic tomography.
In the high-frequency limit, underwater waves propagations are well captured by a low-dimensional Hamiltonian system whose associated trajectories define the so-called acoustic rays (or rays, for short).
Rays have captured my attention, and the many analogies they share with techniques of Celestial Mechanics were certainly what drew me first to the topic (e.g., Chirikov's overlap heuristic to predict the onset of chaos, as in mean-motion planetary resonances).
I currently focus on transport properties of rays through the lens of recurrence.