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Abstract: . For the standard map the homotopically non-trivial invariant curves of rotation number ! satisfying the Bryuno condition are shown to be analytic in the perturbative parameter ", provided j"j is small enough. The radius of convergence ae(!) of the Lindstedt series -- sometimes called critical function of the standard map -- is studied and the relation with the Bryuno function B(!) is derived: the quantity j log ae(!) + 2B(!)j is proved to be bounded uniformily in !. 1. Introduction We... (Update)
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.... tree expansions of the Lindstedt series is due to Eliasson, 13] 6 ALBERTO BERRETTI AND GUIDO GENTILE The trees are de ned as in [1] [2]. Note that, as our perturbation f(x) is more general than the one considered in [1] 2] the mode label u associated to each node u 2 #...
.... for the Lindstedt series of the standard map and the semistandard map share the same dependence on the rotation number (as proved in [2]) is likely to be considered as an accident; 2) to use the results to prove that a bound that in [3] was proved to hold from below holds...
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BibTeX entry: (Update)
Berretti, A. and Gentile, G., Bryuno Function and the Standard Map, Preprint (1998). http://citeseer.ist.psu.edu/berretti98bryuno.html More
@misc{ berretti98bryuno,
author = "A. Berretti and G. Gentile",
title = "Bryuno Function and the Standard Map",
text = "Berretti, A. and Gentile, G., Bryuno Function and the Standard Map, Preprint
(1998).",
year = "1998",
url = "citeseer.ist.psu.edu/berretti98bryuno.html" }
Citations (may not include all citations):116 Graphical Enumeration (context) - Harary, Palmer - 1973
25 Communications in Mathematical Physics (context) - Gallavotti - 1994
18 Methods for the Analysis of the Lindstedt Series for KAM tor.. - Gentile, Mastropietro - 1996
13 Lecture Notes in Mathematics (context) - Schmidt - 1980
10 Scaling Properties for the Radius of Convergence of a Lindst.. - Berretti, Gentile
8 The Brjuno Functions and their Regularity Properties - Marmi, Moussa et al. - 1997
7 The Critical Function for the Semistandard Map (context) - Davie - 1994
7 the Standard Map Critical Function (context) - Marmi, Stark - 1992
5 Majorant series convergence for twistless KAM tori (context) - Gallavotti, Gentile - 1995
1 Annali della Scuola Normale Superiore di Pisa Cl (context) - Bonetto, Gallavotti et al. - 1998
1 eme de Siegel, nombres de Brjuno and polinomes quadratiques,.. (context) - Yoccoz - 1995
1 Renormalization for Analytic Area-Preserving Maps (context) - Davie
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