Small divisor problem in dynamical systems and analytic solutions of a \(q\)-difference equation with a singularity at the origin

DOI10.1007/s00025-010-0060-2zbMath1210.39005OpenAlexW1992318837MaRDI QIDQ606395

Hou Yu Zhao, Jian-guo Si

Publication date: 17 November 2010

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-010-0060-2

zbMATH Keywords

analytic solution\(q\)-difference equationBrjuno conditionsmall divisorDiophantine condition

Mathematics Subject Classification ID

Difference equations, scaling ((q)-differences) (39A13)

Related Items (3)

Small divisors problem in dynamical systems and analytic invariant curves for an iterative equation related to a rational difference equation ⋮ Analytic invariant curves for an iterative equation related to Pielou's equation ⋮ Analytic invariant curves for an iterative equation related to mosquito model

Cites Work

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• On \(p\)-adic functional equations in \(q\)-differences
• Hypergeometric type \(q\)-difference equations: Rodrigues type representation for the second kind solution
• Analytic solutions of general nonlinear functional equations near resonance
• A linear functional equation with a singularity at a fixed point
• A method of functional equations for boundary value problems of continuous media
• The Brjuno functions and their regularity properties
• Galois theory of difference equations
• Arithmetic theory of \(q\)-difference equations. The \(q\)-analogue of Grothendieck-Katz's conjecture on \(p\)-curvatures
• Analytic solutions of a nonlinear iterative equation near neutral fixed points and poles
• Systèmes aux \(q\)-différences singuliers réguliers : classification, matrice de connexion et monodromie. (Regular singular \(q\)-difference systems: Classification, connection matrix and monodromy)
• Gevrey series of arithmetic type. II: Transcendence without transcendence
• Analytic theory of linear \(q\)-difference equations
• Small divisor problem for an analytic \(q\)-difference equation
• An ultrametric version of the Maillet-Malgrange theorem for nonlinear $q$-difference equations
• Hilbert boundary value problem for multiply connected domains
• 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

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