Eventually stable rational functions

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چکیده

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Eventually stable rational functions

For a field K, rational function φ ∈ K(z) of degree at least two, and α ∈ P(K), we study the polynomials in K[z] whose roots are given by the solutions in K to φ(z) = α, where φ denotes the nth iterate of φ. When the number of irreducible factors of these polynomials stabilizes as n grows, the pair (φ,α) is called eventually stable over K. We conjecture that (φ, α) is eventually stable over K w...

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ژورنال

عنوان ژورنال: International Journal of Number Theory

سال: 2017

ISSN: 1793-0421,1793-7310

DOI: 10.1142/s1793042117501263