Scaling properties for the radius of convergence of Lindstedt series: Generalized standard maps
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.
scientific article; zbMATH DE number 1522080