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10. Some Applications and Related Topics

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1834)

Abstract

In this chapter we briefly describe some further applications of the results and methods developed in the preceeding chapters.

  • 10.1 Applications of Quantitative Sard and Transversality Theorems

    • 10.1.1 Maxima of smooth families

    • 10.1.2 Average topological complexity of fibers

    • 10.1.3 Quantitative Kupka-Smale Theorem

    • 10.1.4 Possible Applications in Numerical Analysis

  • 10.2 Semialgebraic Complexity of Functions

    • 10.2.1 Semialgebraic Complexity

    • 10.2.2 Semialgebraic Complexity and Sard Theorem

    • 10.2.3 Complexity of Functions on Infinite-Dimensional Spaces

  • 10.3 Additional Directions

    • 10.3.1 Asymptotic Critical Values of Semialgebraic and Tame Mappings

    • 10.3.2 Morse-Sard Theorem in Sobolev Spaces

    • 10.3.3 From Global to Local: Real Equisingularity

    • 10.3.4 \(\mathcal{C}^k\) Reparametrization of Semialgebraic Sets

    • 10.3.5 Bernstein-Type Inequalities for Algebraic Functions

    • 10.3.6 Polynomial Control Problems

    • 10.3.7 Quantitative Singularity Theory

Keywords

  • Normal Form
  • Periodic Point
  • Algebraic Function
  • Taylor Polynomial
  • Smooth Family

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Yosef Yomdin .

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© 2004 Springer-Verlag

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Yomdin, Y., Comte, G. (2004). 10. Some Applications and Related Topics. In: Tame Geometry with Application in Smooth Analysis. Lecture Notes in Mathematics, vol 1834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40960-1_10

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  • DOI: https://doi.org/10.1007/978-3-540-40960-1_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20612-5

  • Online ISBN: 978-3-540-40960-1

  • eBook Packages: Springer Book Archive