Abstract
In this chapter we make a start on the programme sketched out in Sect. 3.1 by giving the first steps in the classification of differentiable functions. We follow the method suggested by the Transversality Theorem in going from ’generic’ situations to more particular ones. First of all, as the Local Inversion Theorem shows, for a generic function f at a generic point a there is nothing to say: such a function can be written as f(a) + x where x is one member of a system of local coordinates centred at a.
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
© 2000 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Demazure, M. (2000). Classification of Differentiable Functions. In: Bifurcations and Catastrophes. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57134-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-57134-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52118-1
Online ISBN: 978-3-642-57134-3
eBook Packages: Springer Book Archive