Dynamics of the square mapping on the ring of 𝑝-adic integers

DOI10.1090/proc12777zbMath1391.37068arXiv1408.4574OpenAlexW2133334297MaRDI QIDQ2790194

Shilei Fan, Lingmin Liao

Publication date: 3 March 2016

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

Full work available at URL: https://arxiv.org/abs/1408.4574

zbMATH Keywords

\(p\)-adic dynamical systemminimal decompositionsquare mapping

Mathematics Subject Classification ID

Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Non-Archimedean dynamical systems (11S82) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05)

Related Items (6)

Minimality of \(p\)-adic rational maps with good reduction ⋮ Rational map \(ax + 1/x\) on the projective line over \(\mathbb{Q}_2\) ⋮ Rational map 𝑎𝑥+1/𝑥 on the projective line over ℚ_{𝕡} ⋮ Dynamical structures of Chebyshev polynomials on \(\mathbb{Z}_2\) ⋮ Dynamic structures of \(p\)-adic monomials for small primes \(p\) ⋮ Minimality of 5-adic polynomial dynamics

Cites Work

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• On minimal decomposition of \(p\)-adic polynomial dynamical systems
• Characterization of ergodicity of \(p\)-adic dynamical systems by using the van der Put basis
• Toward the ergodicity of \(p\)-adic 1-Lipschitz functions represented by the van der Put series
• Minimal dynamical systems on a discrete valuation domain
• Wieferich's criterion and the abc-conjecture
• On the iteration of certain quadratic maps over GF(\(p\)).
• Uniformly distributed sequences of \(p\)-adic integers
• The graph of the square mapping on the prime fields
• Dynamics of convergent power series on the integral ring of a finite extension of \(\mathbb{Q}_p\)
• Strict ergodicity of affine \(p\)-adic dynamical systems on \(\mathbb Z_p\)
• On ergodicity of \(p\)-adic dynamical systems for arbitrary prime \(p\)
• On minimal decomposition of \(p\)-adic homographic dynamical systems
• Structure of digraphs associated with quadratic congruences with composite moduli
• Minimal polynomial dynamics on the set of 3-adic integers
• Ergodic Transformations in the Space of p-Adic Integers
• On the number of cycles of \(p\)-adic dynamical systems

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