Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of a family of piecewise-linear area-preserving plane maps III.
  Cantor set spectra   This paper studies the behavior under iteration of the maps T_{ab}(x,y) =
(F_{ab}(x)- y, x) of the plane R^2, in which F_{ab}(x)= ax if x>0 and bx if
x<0. These maps are area-preserving homeomorphisms of the plane that map rays
from the origin into rays from the origin. Orbits of the map correspond to
solutions of the nonlinear difference equation x_{n+2}= 1/2(a-b)|x_{n+1}| +
1/2(a+b)x_{n+1} - x_n. This difference equation can be written in an eigenvalue
form for a nonlinear difference operator of Schrodinger type, in which \mu=
1/2(a-b) is viewed as fixed and the energy E=2- 1/2(a+b). The paper studies the
set of parameter values where T_{ab} has at least one nonzero bounded orbit,
which corresponds to an l_{\infty} eigenfunction of the difference operator. It
shows that the for transcendental \mu the set of allowed energy values E for
which there is a bounded orbit is a Cantor set. Numerical simulations suggest
that this Cantor set have positive one-dimensional measure for all real values
of \mu.

11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex