On differentiable functions with isolated critical points

On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions

The set of periodic points of self-maps of intervals has been studied for different reasons. The functions with smaller sets of periodic points are more likely not to share a periodic point. Of course, one has to decide what “big” or “small” means and how to describe this notion. In this direction one would be interested in studying the size of the sets of periodic points of self-maps of an int...

On the Critical Points of Harmonic Functions

Critical Points of Functions on Singular Spaces

We compare and contrast various notions of the “critical locus” of a complex analytic function on a singular space. After choosing a topological variant as our primary notion of the critical locus, we justify our choice by generalizing Lê and Saito’s result that constant Milnor number implies that Thom’s af condition is satisfied.

Critical points of simple functions

Inference on Directionally Differentiable Functions

This paper studies an asymptotic framework for conducting inference on parameters of the form φ(θ0), where φ is a known directionally differentiable function and θ0 is estimated by θ̂n. In these settings, the asymptotic distribution of the plug-in estimator φ(θ̂n) can be readily derived employing existing extensions to the Delta method. We show, however, that the “standard” bootstrap is only cons...