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.
V.I. Arnold (deceased)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media New York
About this chapter
Cite this chapter
Arnold, V.I., Gusein-Zade, S.M., Varchenko, A.N. (2012). The singular index, examples. In: Singularities of Differentiable Maps, Volume 2. Modern Birkhäuser Classics. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8343-6_9
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8343-6_9
Published:
Publisher Name: Birkhäuser, Boston
Print ISBN: 978-0-8176-8342-9
Online ISBN: 978-0-8176-8343-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)