Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integral points and orbits of endomorphisms on the projective plane   We analyze when integral points on the complement of a finite union of curves
in $\mathbb{P}^2$ are potentially dense. We divide the analysis of these affine
surfaces based on their logarithmic Kodaira dimension $\bar{\kappa}$. When
$\bar{\kappa} = -\infty$, we completely characterize the potential density of
integral points in terms of the number of irreducible components on the surface
at infinity and the number of multiple members in a pencil naturally associated
to the surface. When integral points are not potentially dense, we show that
they lie on finitely many effectively computable curves. When $\bar{\kappa} =
0$, we prove that integral points are always potentially dense. The bulk of our
analysis concerns the subtle case of $\bar{\kappa}=1$. We determine the
potential density of integral points in a number of cases and develop tools for
studying integral points on surfaces fibered over a curve. Finally, nondensity
of integral points in the case $\bar{\kappa}=2$ is predicted by the Lang-Vojta
conjecture, to which we have nothing new to add.
  In a related direction, we study integral points in orbits under
endomorphisms of $\mathbb{P}^2$. Assuming the Lang--Vojta conjecture, we prove
that an orbit under an endomorphism $\phi$ of $\mathbb{P}^2$ can contain a
Zariski-dense set of integral points (with respect to some nontrivial effective
divisor) only if there is a nontrivial completely invariant proper
Zariski-closed set with respect to $\phi$. This may be viewed as a
generalization of a result of Silverman on integral points in orbits of
rational functions. We provide many specific examples, and end with some open
problems.

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The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: stat
23
The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph