Scaling properties for the radius of convergence of Lindstedt series: Generalized standard maps
type: Item
instance of: scholarly article
title: Scaling properties for the radius of convergence of Lindstedt series: Generalized standard maps
zbMATH Open document ID: 0997.37027
DOI: 10.1016/S0021-7824(00)00167-7
author: Alberto Berretti
author: Guido Gentile
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2000-10-29T00:00:00Z
review text: The authors deal with a map of the form \[ T_{\varepsilon,f}: \begin{cases} x'= x+y+\varepsilon f(x),\\ y'= y+\varepsilon f(x), \end{cases}\tag{1} \] that generalizes the standard map, where \(f(x)\) is a \(2\pi\)-periodic function of \(x\), analytic in the strip \(S= \{x\mid |\operatorname {Im}x|< \xi\}\). For (1) the radius of convergence of the Lindstedt series describing the homotopically nontrivial curves is proved to satisfy a scaling law as the complexified rotation number tends to a rational value nontangentially to the real axis.
Mathematics Subject Classification ID: 37J10
Mathematics Subject Classification ID: 37E40
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37E45
zbMATH DE Number: 1522080
zbMATH Keywords: generalized standard map
zbMATH Keywords: radius of convergence
zbMATH Keywords: Lindstedt series
zbMATH Keywords: scaling law
zbMATH Keywords: rotation number
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s0021-7824(00)00167-7
OpenAlex ID: W2060452590
description: scientific article; zbMATH DE number 1522080