A DYNAMICAL SYSTEM PROOF OF NIVEN’S THEOREM AND ITS EXTENSIONS

DOI10.1017/s0004972723000448arXiv2304.07823OpenAlexW4381511132WikidataQ121898046 ScholiaQ121898046MaRDI QIDQ6151370

Detchat Samart, Chatchawan Panraksa, Songpon Sriwongsa

Publication date: 12 February 2024

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2304.07823

zbMATH Keywords

arithmetic dynamicsalgebraic numbersNiven's theorem

Mathematics Subject Classification ID

Exponential and trigonometric functions (33B10) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Arithmetic properties of periodic points (37P35)

Cites Work

• The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture
• Cycles of quadratic polynomials and rational points on a genus-2 curve
• Periodic points on an algebraic variety
• Preperiodic points for rational functions defined over a global field in terms of good reduction
• Rational 6-Cycles Under Iteration of Quadratic Polynomials
• Galois theory of periodic orbits of rational maps
• Arithmetic properties of periodic points of quadratic maps, II
• Rational Periodic Points of the Quadratic Function Q c (x) = x 2 + c
• A FINITENESS PROPERTY FOR PREPERIODIC POINTS OF CHEBYSHEV POLYNOMIALS
• On the Rational Values of Trigonometric Functions of Angles that Are Rational in Degrees
• An elementary proof of Niven's theorem via the tangent function
• A Note on Trigonometric Algebraic Numbers
• Integer Sequences
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