Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical degrees of birational transformations of projective surfaces   The dynamical degree $\lambda(f)$ of a birational transformation $f$ measures
the exponential growth rate of the degree of the formulae that define the
$n$-th iterate of $f$. We study the set of all dynamical degrees of all
birational transformations of projective surfaces, and the relationship between
the value of $\lambda(f)$ and the structure of the conjugacy class of $f$. For
instance, the set of all dynamical degrees of birational transformations of the
complex projective plane is a closed and well ordered set of algebraic numbers.

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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an