Criteria of measure-preservation for 1-Lipschitz functions on \(\mathbb F_q[[T]]\) in terms of the van der Put basis and its applications

DOI10.1016/j.ffa.2015.09.007zbMath1402.11141OpenAlexW2163421188MaRDI QIDQ897329

Youngho Jang, Sangtae Jeong, Chunlan Li

Publication date: 17 December 2015

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2015.09.007

zbMATH Keywords

positive characteristicergodic1-Lipschitzvan der Put basismeasure-preservingCarlitz polynomialsdigit derivativesdigit shifts

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Polynomials over finite fields (11T06) Non-Archimedean dynamical systems (11S82) Dynamical systems over non-Archimedean local ground fields (37P20) Non-Archimedean analysis (32P05)

Related Items (9)

On the bijective colouring of Cantor trees based on transducers ⋮ 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 ⋮ Measure-preservation criteria for a certain class of 1-Lipschitz functions on \(\mathbb Z_p\) in Mahler's expansion ⋮ Unnamed Item ⋮ 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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ergodic theory over \(\mathbb F_2 T\)
• 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
• Fourier series, measures and divided power series in the theory of function fields
• The digit principle
• A comparison of the Carlitz and digit derivatives bases in function field arithmetic
• Hyperdifferential operators and continuous functions on function fields
• van der Put basis and \(p\)-adic dynamics
• \(C^n\)-functions over completions of \(\mathbb F_r[T\) at finite places of \(\mathbb F_r(T)\)]
• Uniformly distributed sequences of \(p\)-adic integers
• Criteria of measure-preserving for \(p\)-adic dynamical systems in terms of the van der Put basis
• Characterization of ergodicity of \(T\)-adic maps on \(\mathbb F_2T \) using digit derivatives basis
• Shift operators and two applications to \(\mathbb{F}_qT\)
• Applied algebraic dynamics
• T-functions revisited: new criteria for bijectivity/transitivity
• Minimal polynomial dynamics on the set of 3-adic integers
• Digit derivatives and application to zeta measures
• Interpolation series for continuous functions on π-adic completions of GF(q, x)

This page was built for publication: Criteria of measure-preservation for 1-Lipschitz functions on \(\mathbb F_qT\) in terms of the van der Put basis and its applications