Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of a quasi-quadratic map   We consider the map X defined on the rational numbers given by x --> x *
ceil(x), where ceil(x) denotes the smallest integer greater than or equal to x,
and study the problem of finding, for each rational, the smallest number of
iterations of X that eventually sends it into an integer. Given two natural
numbers M and n, we prove that the set of irreducible fractions with
denominator M whose orbits by X reach an integer in exactly n iterations is a
disjoint union of congruence classes modulo M^n, establishing along the way a
finite procedure to ascertain them. We also describe an efficient algorithm to
decide if an orbit fails to hit an integer until a prescribed number of
iterations, and deduce that the probability that an orbit enters the set of
integers is equal to one.

23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin