Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abstract Similarity, Fractals and Chaos   To prove presence of chaos for fractals, a new mathematical concept of
abstract similarity is introduced. As an example, the space of symbolic strings
on a finite number of symbols is proved to possess the property. Moreover,
Sierpinski fractals, Koch curve as well as Cantor set satisfy the definition. A
similarity map is introduced and the problem of chaos presence for the sets is
solved by considering the dynamics of the map. This is true for Poincare,
Li-Yorke and Devaney chaos, even in multi-dimensional cases. Original numerical
simulations which illustrate the results are delivered.

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The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
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The categories of this paper are: econ
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin