Ergodic theory over \(\mathbb F_2 [[T]]\)

DOI10.1016/j.ffa.2011.11.001zbMath1279.37051arXiv1103.2968OpenAlexW4291296873MaRDI QIDQ413547

Zifeng Yang, Tao Shi, Dong-Dai Lin

Publication date: 7 May 2012

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.2968

zbMATH Keywords

function fieldsergodic theoryformal power seriesCarlitz expansionVan der Put expansion

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Data encryption (aspects in computer science) (68P25) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Power series rings (13J05) Non-Archimedean dynamical systems (11S82) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Dynamical systems over non-Archimedean local ground fields (37P20)

Related Items (17)

Measure-preservation criteria for 1-Lipschitz functions on \(\mathbb F_{q}T\) in terms of the three bases of Carlitz polynomials, digit derivatives, and digit shifts ⋮ The p-adic Theory of Automata Functions ⋮ Ergodic functions over \(\mathbb{F}_q T\) ⋮ Bernoulli maps on \(\mathbf{Z}_p\) in the expansions of van der Put and Mahler ⋮ Ergodicity criteria for non-expanding transformations of 2-adic spheres ⋮ Criteria of measure-preservation for 1-Lipschitz functions on \(\mathbb F_qT\) in terms of the van der Put basis and its applications ⋮ On the characteristic \(p\) valued measure associated to Drinfeld discriminant ⋮ T-functions revisited: new criteria for bijectivity/transitivity ⋮ Measure-preservation criteria for a certain class of 1-Lipschitz functions on \(\mathbb Z_p\) in Mahler's expansion ⋮ Characterization of the ergodicity of 1-Lipschitz functions on \(\mathbb{Z}_2\) using the \(q\)-Mahler basis ⋮ On a nonlinear \(p\)-adic dynamical system ⋮ On recent results of ergodic property for \(p\)-adic dynamical systems ⋮ Shift operators and two applications to \(\mathbb{F}_qT\) ⋮ \(p\)-adic (3, 2)-rational dynamical systems ⋮ Toward the ergodicity of \(p\)-adic 1-Lipschitz functions represented by the van der Put series ⋮ Ergodic functions over \(Z_p\) ⋮ Measure-preservation and the existence of a root of \(p\)-adic 1-Lipschitz functions in Mahler's expansion

Cites Work

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• Uniformly distributed sequences in computer algebra or how to construct program generators of random numbers
• van der Put basis and \(p\)-adic dynamics
• \(C^n\)-functions over completions of \(\mathbb F_r[T\) at finite places of \(\mathbb F_r(T)\)]
• Differentiability in local fields of prime characteristic
• Uniformly distributed sequences of \(p\)-adic integers
• Applied algebraic dynamics
• Fast Software Encryption

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