Toward the ergodicity of \(p\)-adic 1-Lipschitz functions represented by the van der Put series
From MaRDI portal
Publication:740840
DOI10.1016/j.jnt.2013.02.006zbMath1295.37023arXiv1210.5001OpenAlexW2022088456MaRDI QIDQ740840
Publication date: 9 September 2014
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1210.5001
Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Non-Archimedean dynamical systems (11S82) Dynamical systems over non-Archimedean local ground fields (37P20) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30)
Related Items
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 ⋮ Ergodic Products and Powers on Compact Subsets of the $p$-adic Field ⋮ Ergodic functions over \(\mathbb{F}_q T\) ⋮ Bernoulli maps on \(\mathbf{Z}_p\) in the expansions of van der Put and Mahler ⋮ Criteria of measure-preservation for 1-Lipschitz functions on \(\mathbb F_qT\) in terms of the van der Put basis and its applications ⋮ On ergodic transformations on the sphere of 2-adic units ⋮ On some compatible functions on the set of 3-adic integers ⋮ Notes on ergodic \(2\)-adic transformations ⋮ Generalization of Hensel's lemma: finding the roots of \(p\)-adic Lipschitz functions ⋮ Minimality of \(p\)-adic rational maps with good reduction ⋮ Measure-preservation criteria for a certain class of 1-Lipschitz functions on \(\mathbb Z_p\) in Mahler's expansion ⋮ Shift operators and two applications to \(\mathbb{F}_qT\) ⋮ Dynamics of the square mapping on the ring of 𝑝-adic integers ⋮ Rational map 𝑎𝑥+1/𝑥 on the projective line over ℚ_{𝕡} ⋮ Dynamics of some 2-adic isometric transformations ⋮ \(p\)-adic (3, 2)-rational dynamical systems ⋮ Dynamical structures of Chebyshev polynomials on \(\mathbb{Z}_2\) ⋮ Ergodic uniformly differentiable functions modulo \(p\) on \(\mathbb{Z}_p\) ⋮ Ergodic functions over \(Z_p\) ⋮ Measure-preservation and the existence of a root of \(p\)-adic 1-Lipschitz functions in Mahler's expansion ⋮ Minimality of 5-adic polynomial dynamics ⋮ Dynamics of convergent power series on the integral ring of a finite extension of \(\mathbb{Q}_p\) ⋮ On perturbed monomials on 2-adic spheres around 1 ⋮ Characterization of ergodic rational functions on the set of 2-adic units ⋮ On some classes of 1-Lipschitz measure-preserving ergodic functions on ℤp
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Ergodic theory over \(\mathbb F_2 T\)
- 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
- Applied algebraic dynamics
- 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
- Transitive polynomial transformations of residue class rings
- Selected Areas in Cryptography
