Item description for Tame Geometry with Application in Smooth Analysis (Lecture Notes in Mathematics) by Yosef Yomdin...
The Morse-Sard theorem is a rather subtleresult and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proofand also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the studyof polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive.The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation.
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Est. Packaging Dimensions: Length: 9.21" Width: 6.14" Height: 0.42" Weight: 0.63 lbs.
Release Date Mar 5, 2004
ISBN 3540206124 ISBN13 9783540206125
Availability 57 units. Availability accurate as of May 29, 2017 03:25.
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