The singular index, examples
In this chapter we shall prove the additivity of the oscillation index, and describe explicitly the calculation of the singular index In the tables in § 6.1.10. In the second part of the chapter we give an example of the deformation of a critical point. This example illustrates several phenomena. First, the absence of semicontinuity of the oscillation index. Second, the existence of critical points which are complex equivalent but which have distinct singular indices. Third, the existence of a critical point in which the singular index is not equal to the remoteness.
KeywordsTaylor Series Principal Part Opposite Inequality Asymptotic Series Oscillatory Integral
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