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The singular index, examples

  • V. I. Arnold
  • S. M. Gusein-Zade
  • A. N. Varchenko
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

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.

Keywords

Taylor Series Principal Part Opposite Inequality Asymptotic Series Oscillatory Integral 
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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • V. I. Arnold
  • S. M. Gusein-Zade
    • 1
  • A. N. Varchenko
    • 2
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsThe University of North Carolina at Chapel HillChapel HillUSA

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