Smooth geometric linearization conjecture for integrable dynamical systems

In a smooth integrable dynamical system, let the system be defined near a nondegenerate singular point, meaning a singular point satisfying the paper's nondegeneracy condition for integrable systems. A direct product consists of a linear nondegenerate integrable system together with a constant system. Smooth geometric linearization conjecture. Any smooth integrable dynamical system near a nondegenerate singular point is locally geometrically smoothly equivalent to a direct product of a linear nondegenerate integrable system and a constant system. This is the smooth analogue of the analytic geometric-linearization theorem for nondegenerate singular points; the conjecture asserts that the corresponding local normal form persists in the smooth category, where the result is not established in the supplied text.