000 | 03503nam a22005295i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/b94624 _2doi |
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050 | 4 | _aQA564-609 | |
072 | 7 |
_aPBMW _2bicssc |
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072 | 7 |
_aMAT012010 _2bisacsh |
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072 | 7 |
_aPBMW _2thema |
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082 | 0 | 4 |
_a516.35 _223 |
100 | 1 |
_aYomdin, Yosef. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aCC, 190 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1834 |
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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 |