Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Subadditive Ergodic Theorem and generic stretching factors for free
  group automorphisms   Given a free group $F_k$ of rank $k\ge 2$ with a fixed set of free generators
we associate to any homomorphism $\phi$ from $F_k$ to a group $G$ with a
left-invariant semi-norm a generic stretching factor, $\lambda(\phi)$, which is
a non-commutative generalization of the translation number. We concentrate on
the situation when $\phi:F_k\to Aut(X)$ corresponds to a free action of $F_k$
on a simplicial tree $X$, in particular, when $\phi$ corresponds to the action
of $F_k$ on its Cayley graph via an automorphism of $F_k$. In this case we are
able to obtain some detailed ``arithmetic'' information about the possible
values of $\lambda=\lambda(\phi)$. We show that $\lambda \ge 1$ and is a
rational number with $2k\lambda\in \mathbb Z[ \frac{1}{2k-1} ]$ for every
$\phi\in Aut(F_k)$. We also prove that the set of all $\lambda(\phi)$, where
$\phi$ varies over $Aut(F_k)$, has a gap between 1 and $1+\frac{2k-3}{2k^2-k}$,
and the value 1 is attained only for ``trivial'' reasons. Furthermore, there is
an algorithm which, when given $\phi$, calculates $\lambda(\phi)$.

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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn