The behaviour of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue criterion. The results are compared with the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have been proved. The conjectured interpolation of the critical function in terms of the Bryuno function is discussed.

Berretti, A., & Gentile, G. (2004). Scaling of the critical function for the standard map: some numerical results. NONLINEARITY, 17(2), 649-670 [10.1088/0951-7715/17/2/017].

Scaling of the critical function for the standard map: some numerical results

BERRETTI, ALBERTO;
2004-01-19

Abstract

The behaviour of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue criterion. The results are compared with the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have been proved. The conjectured interpolation of the critical function in terms of the Bryuno function is discussed.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
Settore MAT/07 - Fisica Matematica
Settore MAT/08 - Analisi Numerica
English
Con Impact Factor ISI
complex rotation numbers; lindstedt series; renormalization; semistandard; convergence; transition; criterion; behavior; radius; proof
Berretti, A., & Gentile, G. (2004). Scaling of the critical function for the standard map: some numerical results. NONLINEARITY, 17(2), 649-670 [10.1088/0951-7715/17/2/017].
Berretti, A; Gentile, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/55466
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