Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the asymptotic expansion of maps with disconnected Julia set   We study the asymptotic expansion of smooth one-dimensional maps. We give an
example of an interval map for which the optimal shrinking of components
exponential rate is not attained for any neighborhood of a certain fixed point
in the boundary of a periodic Fatou component. We prove a general result
asserting that, when this happens the components do shrink exponentially,
although the rate is not the optimal one. Finally, we give an example of a
polynomial with real coefficients, such that all its critical points in the
complex plane are real, and such that its asymptotic expansion as a complex map
is strictly smaller than its asymptotic expansion as a real map.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn