LEADER 04125nam 22007455 450 001 9910144619803321 005 20251117004511.0 010 $a3-540-40960-2 024 7 $a10.1007/b94624 035 $a(CKB)1000000000230916 035 $a(SSID)ssj0000327117 035 $a(PQKBManifestationID)11239533 035 $a(PQKBTitleCode)TC0000327117 035 $a(PQKBWorkID)10301588 035 $a(PQKB)10237520 035 $a(DE-He213)978-3-540-40960-1 035 $a(MiAaPQ)EBC6303921 035 $a(MiAaPQ)EBC5591388 035 $a(Au-PeEL)EBL5591388 035 $a(OCoLC)56338034 035 $a(PPN)155202529 035 $a(EXLCZ)991000000000230916 100 $a20121227d2004 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTame Geometry with Application in Smooth Analysis /$fby Yosef Yomdin, Georges Comte 205 $a1st ed. 2004. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2004. 215 $a1 online resource (CC, 190 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1834 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-20612-4 320 $aIncludes bibliographical references (pages 173-186). 327 $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. 330 $aThe Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1834 606 $aGeometry, Algebraic 606 $aMeasure theory 606 $aFunctions of real variables 606 $aFunctions of complex variables 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198 615 0$aGeometry, Algebraic. 615 0$aMeasure theory. 615 0$aFunctions of real variables. 615 0$aFunctions of complex variables. 615 14$aAlgebraic Geometry. 615 24$aMeasure and Integration. 615 24$aReal Functions. 615 24$aSeveral Complex Variables and Analytic Spaces. 676 $a515.42 700 $aYomdin$b Yosef$4aut$4http://id.loc.gov/vocabulary/relators/aut$0282756 702 $aComte$b Georges$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144619803321 996 $aTame Geometry with Application in Smooth Analysis$92541500 997 $aUNINA