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- catalog abstract "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.".
- catalog contributor b13148197.
- catalog contributor b13148198.
- catalog created "c2004.".
- catalog date "2004".
- catalog date "c2004.".
- catalog dateCopyrighted "c2004.".
- catalog description "Includes bibliographical references (p. [173]-186).".
- catalog description "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.".
- catalog description "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.".
- catalog extent "viii, 186 p. :".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540206124 (pbk.)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1834.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; v. 1834".
- catalog issued "2004".
- catalog issued "c2004.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "Differential equations, partial.".
- catalog subject "Geometry, algebraic.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1834".
- catalog subject "Smoothing (Numerical analysis)".
- catalog subject "Tame geometry.".
- catalog tableOfContents "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.".
- catalog title "Tame geometry with application in smooth analysis / Yosef Yomdin, Georges Comte.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".