Tame geometry with application in smooth analysis Yosef Yomdin; Georges Comte
Materialtyp:
TextSprache: Englisch Reihen: ; 183400 | Lecture notes in mathematics ; 1834Verlag: Berlin Heidelberg [u.a.] Springer 2004Beschreibung: VIII, 186 S graph. DarstInhaltstyp: - Text
- ohne Hilfsmittel zu benutzen
- Band
- 3540206124
- Measure theory
- Arithmetical algebraic geometry
- Smoothing (Numerical analysis)
- Differentialtopologie
- Differenzierbare Funktion
- Dynamisches System
- Fraktalgeometrie
- Integralgeometrie
- Kritischer Punkt <Mathematik>
- Maßtheorie
- Polynomiale Abbildung
- Semialgebraische Menge
- Singularität <Mathematik>
- Semialgebraische Menge
- Polynomiale Abbildung
- Maßtheorie
- Integralgeometrie
- Differenzierbare Funktion
- Kritischer Punkt Mathematik
- Fraktalgeometrie
- Differentialtopologie
- Singularität Mathematik
- Dynamisches System
- QA3
- 17,1
- SI 850
- SK 660
- *14P10
- 14-02
- 14Q20
- 26B15
- 32S15
- 31.41
- 31.51
- 31.43
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Gebäude E2 3 (UdS Campusbibliothek für Informatik und Mathematik) | Campusbibliothek für Informatik und Mathematik (E2 3) | Series (GF) | LNM 1834 (Regal durchstöbern(Öffnet sich unterhalb)) | Verfügbar | 2202000369783 |
Literaturverz. S. [173] - 186
The Morse-Sard theorem is a rather subtleresult 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 proofand also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the studyof 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. TOC: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
Yomdin, Yosef: Tame Geometry with Application in Smooth Analysis
Archivierung/Langzeitarchivierung gewährleistet PEBW pdager DE-31