The behavior of orbits of the Hamilton vector field of the principal symbol of a second-order hyperbolic differential operator is discussed. In our previous paper, assuming that is noneffectively hyperbolic on the doubly characteristic manifold of , we have proved that if on with the Hamilton vector field of some specified , then there exists a bicharacteristic landing on tangentially. The aim of this paper is to provide a much more simple proof of this result since the previous proof was fairly long and rather complicated.
"A simple proof of the existence of tangent bicharacteristics for noneffectively hyperbolic operators." Kyoto J. Math. 55 (2) 281 - 297, June 2015. https://doi.org/10.1215/21562261-2871758