Settled polynomials over finite fields

We study the factorization into irreducibles of iterates of a quadratic polynomial f settled when the factorization of its n is dominated by ``stable'' polynomials, namely those that are irreducible under post-composition by any iterate of f and that the critical orbit also gives informati...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2012-06, Vol.140 (6), p.1849-1863
Main Authors: JONES, RAFE, BOSTON, NIGEL
Format: Article
Language:English
Subjects:
Critical points
Descendants
Eigenvalues
Factorization
Integers
Markov processes
Polynomials
Quadratic polynomials
Vertices
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Summary:We study the factorization into irreducibles of iterates of a quadratic polynomial f settled when the factorization of its n is dominated by ``stable'' polynomials, namely those that are irreducible under post-composition by any iterate of f and that the critical orbit also gives information about the splitting of non-stable polynomials under post-composition by iterates of f and conjecture that its limiting distribution describes the full factorization of large iterates of f defined over a finite field are settled. We give several types of evidence for our conjecture.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2011-11054-2