Small divisors problem in dynamical systems and analytic solutions of the Shabat equation

DOI10.1016/J.JMAA.2010.01.025zbMath1191.37029OpenAlexW2064803767MaRDI QIDQ961101

Xianlong Li, Jian-guo Si

Publication date: 29 March 2010

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.2010.01.025

zbMATH Keywords

Schrödinger operatoranalytic solutionGevrey classesSiegel's methodDavie's LemmaShabat equation

Mathematics Subject Classification ID

Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Functional equations for complex functions (39B32) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

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 Ricker-type second-order equation ⋮ Analytic solutions of a second-order functional differential equation

Cites Work

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• The Brjuno functions and their regularity properties
• An existence result for the Shabat equation
• Coherent states of the \(q\)-Weyl algebra
• Construction of reflectionless potentials with infinite discrete spectrum
• Self-similar potentials and the \(q\)-oscillator algebra at roots of unity
• Existence and uniqueness of analytic solutions of the Shabat equation
• The infinite-dimensional dressing dynamical system
• Linearization of analytic and non-analytic germs of diffeomorphisms of $({\mathbb C},0)$

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