Tangential approximation of analytic sets

Algebraic Approximation of Germs of Real Analytic Sets

Two subanalytic subsets of Rn are s-equivalent at a common point, say O, if the Hausdorff distance between their intersections with the sphere centered at O of radius r goes to zero faster than rs. In the present paper we investigate the existence of an algebraic representative in every sequivalence class of subanalytic sets. First we prove that such a result holds for the zero-set V (f) of an ...

Normal Forms of Analytic Perturbations of Quasihomogeneous Vector Fields: Rigidity, Invariant Analytic Sets and Exponentially Small Approximation

Analytic Approximation Theorem

Analytic sets under attack

A point in Baire space is found for which the first derived ω-limit set is not Borel, whilst the second is empty. A second point is found for which the sequence of derived ω-limit sets does not stabilise until the first uncountable ordinal. The two points are recursive.

Approximation of Singularity Sets with Analytic Graphs over the Ball in C

Let h be a smooth function on the ball in C2 whose gradient has length less than or equal to 1. We show that if h is uniformly near an analytic function on every complex affine one-dimensional slice then it must be near some function analytic on the whole ball. We use this to show the following: a singularity set over the ball which is near the graph of a function h with |∇h| ≤ 1 must be near t...