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 &...
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| Formatua: | Livre numérique |
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Berlin [etc.] :
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Cham : Springer Nature |
| Saila: | Lecture notes in mathematics
1834 |
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| Edition sous un autre format: | • Tame geometry with application in smooth analysis, Yosef Yomdin, Georges Comte, 2004, Berlin, Springer, 1 vol. (VIII-186 p.), Lecture notes in mathematics, 3-540-20612-4 • Tame Geometry with Application in Smooth Analysis, Texte imprimé, 9783662214480 |
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| 100 | 1 | |a Yomdin, Yosef. | |
| 245 | 1 | 0 | |a Tame Geometry with Application in Smooth Analysis |c Yosef Yomdin, Georges Comte. |
| 260 | |a Berlin [etc.] : |b Springer. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Lecture notes in mathematics |v 1834 |x 1617-9692 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 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 | |a Théorie de la mesure | ||
| 650 | |a Géométrie algébrique arithmétique | ||
| 650 | |a Lissage (analyse numérique) | ||
| 650 | |a Mathématiques | ||
| 650 | |a Géométrie algébrique | ||
| 650 | |a Fonctions de plusieurs variables complexes | ||
| 650 | |a Fonctions d'une variable réelle | ||
| 700 | 1 | |a Comte, Georges, |d 1947- |4 aut | |
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| 776 | 0 | |t Tame Geometry with Application in Smooth Analysis |b Texte imprimé |z 9783662214480 | |
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