Symmetrization of Hyperbolic Systems with Non-degenerate Characteristics

We study symmetrization of hyperbolic first order systems. To be precise, generalizing non-degenerate double characteristics, we define non degenerate characteristics of any order. Then, assuming that the reference characteristic is non degenerate, we prove that the system is smoothly symmetrizable near the characteristic. Applying this result, we also show that non degenerate characteristics can not be removed by hyperbolic perturbations.