000 03503nam a22005295i 4500
001 978-3-540-40960-1
003 DE-He213
005 20190213151450.0
007 cr nn 008mamaa
008 121227s2004 gw | s |||| 0|eng d
020 _a9783540409601
_9978-3-540-40960-1
024 7 _a10.1007/b94624
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aYomdin, Yosef.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTame Geometry with Application in Smooth Analysis
_h[electronic resource] /
_cby Yosef Yomdin, Georges Comte.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2004.
300 _aCC, 190 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1834
505 0 _aPreface -- 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 _aThe 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 _aGeometry, algebraic.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aMeasure and Integration.
_0http://scigraph.springernature.com/things/product-market-codes/M12120
650 2 4 _aReal Functions.
_0http://scigraph.springernature.com/things/product-market-codes/M12171
650 2 4 _aSeveral Complex Variables and Analytic Spaces.
_0http://scigraph.springernature.com/things/product-market-codes/M12198
700 1 _aComte, Georges.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540206125
776 0 8 _iPrinted edition:
_z9783662214480
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1834
856 4 0 _uhttps://doi.org/10.1007/b94624
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10772
_d10772