Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transformations between attractors of hyperbolic iterated function
  systems   This paper is in the form of an essay. It defines fractal tops and code space
structures associated with set-attractors of hyperbolic iterated function
systems (IFSs). The fractal top of an IFS is associated with a certain shift
invariant subspace of code space, whence the entropy of the IFS, and of its
set-attractor, may be defined. Given any ordered pair of hyperbolic IFSs, each
with the same number of maps, there is a natural transformation, constructed
with the aid of fractal tops, whose domain is the attractor A of the first IFS
and whose range is contained in the attractor B of the second IFS. This
transformation is continuous when the code space structure of the IFS is
"contained in" the code space structure of the second IFS, and is a
homeomorphism between A and B when the code space structures are the same.
Conversely, if two IFS are homeomorphic then they possess the same code space
structure. Hence we obtain that two IFS attractors are homeomorphic then they
have the same entropy. Several examples of fractal transformations and fractal
homeomphisms are given.

15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int