Chebyshev action on finite fields

DOI10.1016/j.disc.2013.10.014zbMath1278.05111arXiv1209.4396OpenAlexW2159936308MaRDI QIDQ393171

T. Alden Gassert

Publication date: 16 January 2014

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.4396

zbMATH Keywords

finite fieldChebyshev polynomialprime decompositioniterated polynomialpost-critically finite map

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Directed graphs (digraphs), tournaments (05C20)

Related Items (14)

Tangent-Chebyshev maps over finite fields: new properties and functional graphs ⋮ Periodic points and tail lengths of split polynomial maps modulo primes ⋮ Rédei Actions on Finite Fields and Multiplication Map in Cyclic Group ⋮ On the functional graph of the power map over finite groups ⋮ Functional graphs of polynomials over finite fields ⋮ On the functional graph of \(f(X)=c(X^{q+1} + aX^2)\) over quadratic extensions of finite fields ⋮ The graph structure of Chebyshev polynomials over finite fields and applications ⋮ The functional graph of linear maps over finite fields and applications ⋮ Discriminants of simplest \(3^n\)-tic extensions ⋮ Value sets of Lattès maps over finite fields ⋮ Dynamics of the \(a\)-map over residually finite Dedekind domains and applications ⋮ A BRIEF NOTE ON SOME INFINITE FAMILIES OF MONOGENIC POLYNOMIALS ⋮ Discriminants of special quadrinomials ⋮ Discriminants of Chebyshev radical extensions

Cites Work

• On the iteration of certain quadratic maps over GF(\(p\)).
• Graphs associated with the map \(x\mapsto x+x^{-1}\) in finite fields of characteristic three and five
• Graphs associated with the map 𝑥\𝑚𝑎𝑝𝑠𝑡𝑜𝑥+𝑥⁻¹ in finite fields of characteristic two
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