Small denominators in complex \(p\)-adic dynamics
type: Item
instance of: scholarly article
title: Small denominators in complex \(p\)-adic dynamics
zbMATH Open document ID: 0998.37009
DOI: 10.1016/S0019-3577(01)80024-0
published in: Indagationes Mathematicae. New Series
publication date: 2002-06-23T00:00:00Z
review text: The author considers the problem of small denominators for analytic maps of the algebraic closure of a \(p\)-adic field. The size of the coefficients of the power series that conjugates a map with a neutral fixed point to its linear part is estimated. Such estimate is optimal, leading to an expression for the radius of the Siegel disc. The computation is more involved than in the \(p\)-adic case.
reviewed by: Franco Vivaldi
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 11S85
zbMATH DE Number: 1758183
zbMATH Keywords: \(p\)-adic dynamics
zbMATH Keywords: small denominators
zbMATH Keywords: arithmetic dynamics
author: Andrei Khrennikov
MaRDI profile type: Publication
cites work: \(p\)-adic probability and an interpretation of negative probabilities in quantum mechanics.
cites work: \(p\)-adic dynamical systems
cites work: P-ADIC DYNAMICAL SYSTEMS AND NEURAL NETWORKS
cites work: Geometry of \(p\)-adic Siegel discs
cites work: Q4002072
cites work: Round-off errors andp-adic numbers
cites work: Attractors of random dynamical systems over \(p\)-adic numbers and a model of ``noisy'' cognitive processes.
cites work: Q4881419
cites work: Q4841577
cites work: \(p\)-adic stochastics and Dirac quantization with negative probabilities
cites work: Statistical interpretation of p-adic quantum theories with p-adic valued wave functions
cites work: Q4211216
cites work: Q4698281
cites work: Sen's Theorem on Iteration of Power Series
cites work: Q3701527
cites work: Q3993082
cites work: Ergodicity of \(p\)-adic multiplications and the distribution of Fibonacci numbers
cites work: Polynomial cycles in certain local domains
cites work: Q3346515
cites work: p-adic dynamics
cites work: Q4003475
cites work: p-adic space-time and string theory
cites work: Q3931654
cites work: p-adic Chaos and Random Number Generation
description: scientific article; zbMATH DE number 1758183