Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic points of post-critically algebraic endomorphisms   A holomorphic endomorphism of $\mathbb{CP}^n$ is post-critically algebraic if
its critical hypersurfaces are periodic or preperiodic. This notion generalizes
the notion of post-critically finite rational maps in dimension one. We will
study the eigenvalues of the differential of such a map along a periodic cycle.
When $n=1$, a well-known fact is that the eigenvalue along a periodic cycle of
a post-critically finite rational map is either superattracting or repelling.
We prove that when $n=2$ the eigenvalues are still either superattracting or
repelling. This is an improvement of a result by Mattias Jonsson. When $n\geq
2$ and the cycle is outside the post-critical set, we prove that the
eigenvalues are repelling. This result improves one which was already obtained
by Fornaess and Sibony under a hyperbolicity assumption on the complement of
the post-critical set.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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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: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: cs