Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parity sequences of the 3x+1 map on the 2-adic integers and Euclidean
  embedding   In this paper, we consider the one-to-one correspondence between a 2-adic
integer and its parity sequence under iteration of the so-called "3x+1" map.
First, we prove a new formula for the inverse transform. Next, we briefly
review what is known about the induced automorphism and study its dynamics on
the 2-adic integers. We find that it is ergodic on many small odd invariant
sets, and that it has two odd cycles of period 2 in addition to its two odd
fixed points. Finally, a plane embedding is presented, for which we establish
affine self-similarity by using functional equations.

19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th