Some Applications and Related Topics

Yomdin Y.

Table of contents :
10.1.1 Maxima of smooth families……Page 2
10.1.2 Average topological complexity of fibers……Page 3
10.1.3 Quantitative Kupka-Smale Theorem……Page 4
10.1.4 Possible Applications in Numerical Analysis……Page 6
10.2 Semialgebraic Complexity of Functions……Page 18
10.2.1 Semialgebraic Complexity……Page 19
10.2.2 Semialgebraic Complexity and Sard Theorem……Page 22
10.2.3 Complexity of Functions on Infinite-Dimensional Spaces……Page 23
10.3.1 Asymptotic Critical Values of Semialgebraic and Tame Mappings……Page 25
10.3.2 Morse-Sard Theorem in Sobolev Spaces……Page 26
10.3.3 From Global to Local: Real Equisingularity……Page 27
10.3.4 $C^k$ Reparametrization of Semialgebraic Sets……Page 28
10.3.5 Bernstein-Type Inequalities for Algebraic Functions……Page 29
10.3.6 Polynomial Control Problems……Page 31
10.3.7 Quantitative Singularity Theory……Page 35