Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential Diophantine approximation and symbolic dynamics   We extend the key formula which intertwines multiplicative Markoff-Lagrange
spectrum and symbolic dynamics. The proof uses complex analysis and elucidates
the strategy of the problem. Moreover, the new method applies to a wide variety
of polynomials possibly having multiple roots. We derive several consequences
of this formula, which are expected on the Markoff-Lagrange spectrum.

20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph