Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Typical orbits of quadratic polynomials with a neutral fixed point:
  non-Brjuno type   We investigate the quantitative and analytic aspects of the near-parabolic
renormalization scheme introduced by Inou and Shishikura in 2006. These provide
techniques to study the dynamics of some holomorphic maps of the form $f(z) =
e^{2\pi i \alpha} z + \mathcal{O}(z^2)$, including the quadratic polynomials
$e^{2\pi i \alpha} z+z^2$, for some irrational values of $\alpha$. The main
results of the paper concern fine-scale features of the measure-theoretic
attractors of these maps, and their dependence on the data. As a bi-product, we
establish an optimal upper bound on the size of the maximal linearization
domain in terms of the Siegel-Brjuno-Yoccoz series of $\alpha$.

10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph