Proc. Japan Acad. Ser. A Math. Sci. 100 (7), 37-42, (July 2024) DOI: 10.3792/pjaa.100.008
KEYWORDS: Hamilton map, time function, Effectively hyperbolic critical point, Cauchy problem, 35L10, 35L15, 35L80
Geometric aspects of effectively hyperbolic critical points on time $t=0$ are discussed assuming that the characteristic roots are real on one side of time $t$, namely time is positive. In particular, we aim to elucidate the differences in the geometric aspects of effectively hyperbolic critical points on time $t=0$ when the characteristic roots are real on both the positive and negative sides of time.