On the iterations of certain maps \(X \mapsto K \cdot(X + X^{- 1})\) over finite fields of odd characteristic

DOI10.1016/j.jnt.2014.02.024zbMath1317.37114arXiv1304.3283OpenAlexW1645919873WikidataQ114157535 ScholiaQ114157535MaRDI QIDQ403298

J. Herrera, H. S. Yoon

Publication date: 29 August 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.3283

zbMATH Keywords

dynamical systemselliptic curvesfinite fieldsarithmetic dynamics

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05)

Related Items (5)

Sequences of irreducible polynomials over odd prime fields via elliptic curve endomorphisms ⋮ Rédei Actions on Finite Fields and Multiplication Map in Cyclic Group ⋮ The graph structure of Chebyshev polynomials over finite fields and applications ⋮ Dynamics of the \(a\)-map over residually finite Dedekind domains and applications ⋮ Sequences of irreducible polynomials without prescribed coefficients over odd prime fields

Cites Work

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• The explicit construction of irreducible polynomials over finite fields
• On the iteration of certain quadratic maps over GF(\(p\)).
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• The graph of the square mapping on the prime fields
• Graphs associated with the map \(x\mapsto x+x^{-1}\) in finite fields of characteristic three and five
• On the construction of irreducible self-reciprocal polynomials over finite fields
• Graphs associated with the map 𝑥\𝑚𝑎𝑝𝑠𝑡𝑜𝑥+𝑥⁻¹ in finite fields of characteristic two
• Monomial dynamical systems of dimension one over finite fields
• Group structure of elliptic curves over finite fields.

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