Tame Geometry with Application in Smooth Analysis

The Morse-Sard theorem is a rather subtle result 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 proof and also an &...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Yomdin, Yosef (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Comte, Georges (http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
Έκδοση:1st ed. 2004.
Σειρά:Lecture Notes in Mathematics, 1834
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 03598nam a2200553 4500
001 978-3-540-40960-1
003 DE-He213
005 20191024111612.0
007 cr nn 008mamaa
008 121227s2004 gw | s |||| 0|eng d
020 |a 9783540409601  |9 978-3-540-40960-1 
024 7 |a 10.1007/b94624  |2 doi 
040 |d GrThAP 
050 4 |a QA564-609 
072 7 |a PBMW  |2 bicssc 
072 7 |a MAT012010  |2 bisacsh 
072 7 |a PBMW  |2 thema 
082 0 4 |a 516.35  |2 23 
100 1 |a Yomdin, Yosef.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Tame Geometry with Application in Smooth Analysis  |h [electronic resource] /  |c by Yosef Yomdin, Georges Comte. 
250 |a 1st ed. 2004. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2004. 
300 |a CC, 190 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 1834 
505 0 |a Preface -- Introduction and Content -- Entropy -- Multidimensional Variations -- Semialgebraic and Tame Sets -- Some Exterior Algebra -- Behavior of Variations under Polynomial Mappings -- Quantitative Transversality and Cuspidal Values for Polynomial Mappings -- Mappings of Finite Smoothness -- Some Applications and Related Topics -- Glossary -- References. 
520 |a The Morse-Sard theorem is a rather subtle result 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 proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of 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. 
650 0 |a Algebraic geometry. 
650 0 |a Measure theory. 
650 0 |a Functions of real variables. 
650 0 |a Functions of complex variables. 
650 1 4 |a Algebraic Geometry.  |0 http://scigraph.springernature.com/things/product-market-codes/M11019 
650 2 4 |a Measure and Integration.  |0 http://scigraph.springernature.com/things/product-market-codes/M12120 
650 2 4 |a Real Functions.  |0 http://scigraph.springernature.com/things/product-market-codes/M12171 
650 2 4 |a Several Complex Variables and Analytic Spaces.  |0 http://scigraph.springernature.com/things/product-market-codes/M12198 
700 1 |a Comte, Georges.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783540206125 
776 0 8 |i Printed edition:  |z 9783662214480 
830 0 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 1834 
856 4 0 |u https://doi.org/10.1007/b94624  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
912 |a ZDB-2-LNM 
912 |a ZDB-2-BAE 
950 |a Mathematics and Statistics (Springer-11649)