Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the complexity of algebraic numbers II. Continued fractions   The continued fraction expansion of an irrational number $\alpha$ is
eventually periodic if and only if $\alpha$ is a quadratic irrationality.
However, very little is known regarding the size of the partial quotients of
algebraic real numbers of degree at least three. Because of some numerical
evidence and a belief that these numbers behave like most numbers in this
respect, it is often conjectured that their partial quotients form an unbounded
sequence. More modestly, we may expect that if the sequence of partial
quotients of an irrational number $\alpha$ is, in some sense, "simple", then
$\alpha$ is either quadratic or transcendental. The term "simple" can of course
lead to many interpretations. It may denote real numbers whose continued
fraction expansion has some regularity, or can be produced by a simple
algorithm (by a simple Turing machine, for example), or arises from a simple
dynamical system... The aim of this paper is to present in a unified way
several new results on these different approaches of the notion of
simplicity/complexity for the continued fraction expansion of algebraic real
numbers of degree at least three.

29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph