Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new proof of Bronshtein's theorem   We give a new self-contained proof of Bronshtein's theorem, that any
continuous root of a $C^{n-1,1}$-family of monic hyperbolic polynomials of
degree $n$ is locally Lipschitz, and obtain explicit bounds for the Lipschitz
constant of the root in terms of the coefficients. As a by-product we reprove
the recent result of Colombini, Orr\'u, and Pernazza, that a $C^n$-curve of
hyperbolic polynomials of degree $n$ admits a $C^1$-system of its roots.

32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org