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This article is cited in 6 scientific papers (total in 6 papers)
Renormalization Group and Field Theoretic Techniques for the Analysis of the Lindstedt Series
A. Berrettia, G. Gentileb a Dipartimento di Matematica,
II Università di Roma (Tor Vergata),
Via della Ricerca Scientifica, 00133 Roma, Italy
b Dipartimento di Matematica,
Università di Roma 3,
Largo S. Leonardo Murialdo 1, 00146 Roma, Italy
Abstract:
The Lindstedt series were introduced in the XIXth century in Astronomy to study perturbatively quasi-periodic motions in Celestial Mechanics. In Mathematical Physics, after getting the attention of Poincaré, who studied them widely by pursuing to all orders the analysis of Lindstedt and Newcomb, their use was somehow superseded by other methods usually referred to as KAM theory. Only recently, after Eliasson's work, they have been reconsidered as a tool to prove KAM-type results, in a spirit close to that of the Renormalization Group in quantum field theory. Following this new approach we discuss here the use of the Lindstedt series in the context of some model problems, like the standard map and natural generalizations, with particular attention to the properties of analyticity in the perturbative parameter.
Received: 31.10.2001
Citation:
A. Berretti, G. Gentile, “Renormalization Group and Field Theoretic Techniques for the Analysis of the Lindstedt Series”, Regul. Chaotic Dyn., 6:4 (2001), 389–420
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https://www.mathnet.ru/eng/rcd853 https://www.mathnet.ru/eng/rcd/v6/i4/p389
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