Small divisor problem for an analytic \(q\)-difference equation

DOI10.1016/j.jmaa.2007.12.010zbMath1146.39035OpenAlexW1990907215MaRDI QIDQ2481879

Bing Xu, Wei Nian Zhang

Publication date: 15 April 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.12.010

zbMATH Keywords

analytic solution\(q\)-difference equationBrjuno conditioniterative equationsmall divisorDiophantine condition

Mathematics Subject Classification ID

Iteration theory, iterative and composite equations (39B12) Difference equations, scaling ((q)-differences) (39A13) Functional equations for complex functions (39B32)

Related Items (4)

Small divisor problem in dynamical systems and analytic solutions of a \(q\)-difference equation with a singularity at the origin ⋮ Formal solutions of the generalized Dhombres functional equation with value one at zero ⋮ The existence of Siegel disks for the Cremona map ⋮ Analytic solutions of an iterative differential equation under Brjuno condition

Cites Work

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• Hypergeometric type \(q\)-difference equations: Rodrigues type representation for the second kind solution
• Analytic solutions of general nonlinear functional equations near resonance
• Galois theory of difference equations
• Analytic solutions of a nonlinear iterative equation near neutral fixed points and poles
• Iteration of analytic functions
• Building blocks for quadratic Julia sets
• Invariant curves for planar mappings
• Discreteq-derivatives and symmetries ofq-difference equations
• Linearization of analytic and non-analytic germs of diffeomorphisms of $({\mathbb C},0)$
• Analytic Solutions of aq-Difference Equation and Applications to Iterative Equations^*
• The critical function for the semistandard map
• Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann
• Discussion on the differentiable solutions of the iterated equation

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