Abstract
We study here the multidimensional variations of the image under a polynomial mapping of a semialgebraic set. We bound from above the i-th variation of the image by the i-th variation of the set and by the i-th Jacobian. This allows us to prove the quantitative Sard theorem for polynomial functions. We also define and study the “variations” of a polynomial mapping, and we finally bound from below the variation of the image.
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
Corresponding author
Rights and permissions
Copyright information
© 2004 Springer-Verlag
About this chapter
Cite this chapter
Yomdin, Y., Comte, G. (2004). 7. Behaviour of Variations under Polynomial Mappings. In: Tame Geometry with Application in Smooth Analysis. Lecture Notes in Mathematics, vol 1834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40960-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-40960-1_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20612-5
Online ISBN: 978-3-540-40960-1
eBook Packages: Springer Book Archive