On the length of critical orbits of stable quadratic polynomials

DOI10.1090/S0002-9939-10-10404-3zbMath1268.11155arXiv0909.3972OpenAlexW2017322818MaRDI QIDQ3581090

Alina Ostafe, Igor E. Shparlinski

Publication date: 16 August 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.3972

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Estimates on character sums (11L40) Dynamical systems over finite ground fields (37P25)

Related Items (9)

ON STABLE QUADRATIC POLYNOMIALS ⋮ Settled polynomials over finite fields ⋮ An estimate on the number of stable quadratic polynomials ⋮ An iterative construction of irreducible polynomials reducible modulo every prime ⋮ Full orbit sequences in affine spaces via fractional jumps and pseudorandom number generation ⋮ On the complexity of exact counting of dynamically irreducible polynomials ⋮ Irreducibility of iterates of post-critically finite quadratic polynomials over \(\mathbb{Q}\) ⋮ Irreducible polynomials over finite fields produced by composition of quadratics ⋮ On Sets of Irreducible Polynomials Closed by Composition

Cites Work

• Settled polynomials over finite fields
• The density of prime divisors in the arithmetic dynamics of quadratic polynomials
• Irreducibility of the iterates of a quadratic polynomial over a field
• Stabilité des polynômes
• Iterated Galois towers, their associated martingales, and the $p$-adic Mandelbrot set
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