Measure-preservation criteria for a certain class of 1-Lipschitz functions on \(\mathbb Z_p\) in Mahler's expansion

DOI10.3934/dcds.2017160zbMath1391.37074OpenAlexW2606318240MaRDI QIDQ524521

Sangtae Jeong, Chunlan Li

Publication date: 3 May 2017

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2017160

zbMATH Keywords

measure-preserving mapMahler basis\(p\)-adic integervan der Put basis

Mathematics Subject Classification ID

Related Items (11)

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 ⋮ A new class of \(p\)-adic Lipschitz functions and multidimensional Hensel's lemma ⋮ The p-adic Theory of Automata Functions ⋮ Mahler coefficients of some 3-adic ergodic functions ⋮ Ergodic functions over \(\mathbb{F}_q T\) ⋮ Bernoulli maps on \(\mathbf{Z}_p\) in the expansions of van der Put and Mahler ⋮ Mahler coefficients of 1-Lipschitz measure-preserving functions on ℤp ⋮ Shadowing and stability in \(p\)-adic dynamics ⋮ Mahler coefficients of uniformly differentiable functions modulo p ⋮ 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

• Ergodic theory over \(\mathbb F_2 T\)
• Relating the quantum mechanics of discrete systems to standard canonical quantum mechanics
• 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
• Quantization causes waves: smooth finitely computable functions are affine
• Criteria of measure-preservation for 1-Lipschitz functions on \(\mathbb F_qT\) in terms of the van der Put basis and its applications
• van der Put basis and \(p\)-adic dynamics
• Uniformly distributed sequences of \(p\)-adic integers
• Criteria of measure-preserving for \(p\)-adic dynamical systems in terms of the van der Put basis
• On measure-preserving functions over \(\mathbb Z_3\)
• Characterization of ergodicity of \(T\)-adic maps on \(\mathbb F_2T \) using digit derivatives basis
• The non-Archimedean theory of discrete systems
• Shift operators and two applications to \(\mathbb{F}_qT\)
• Characterization of the ergodicity of 1-Lipschitz functions on \(\mathbb{Z}_2\) using the \(q\)-Mahler basis
• Applied algebraic dynamics
• Zur Theorie der Polynomtransformationen und Permutationspolynome
• T-functions revisited: new criteria for bijectivity/transitivity
• An Interpolation Series for Continuous Functions of a p-adic Variable.
• Minimal polynomial dynamics on the set of 3-adic integers
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Measure-preservation criteria for a certain class of 1-Lipschitz functions on \(\mathbb Z_p\) in Mahler's expansion