We discuss a Nash-Moser/KAM algorithm for the construction of invariant tori for tame vector fields. Similar algorithms have been studied widely both in finite and infinite dimensional contexts: we are particularly interested in the second case where tameness properties of the vector fields become very important. We focus on the formal aspects of the algorithm and particularly on the minimal hypotheses needed for convergence. We discuss various applications where we show how our algorithm allows one to reduce to solving only linear forced equations. We remark that our algorithm works at the same time in analytic and Sobolev classes.

Corsi, L., Feola, R., Procesi, M. (2019). Finite dimensional invariant KAM tori for tame vector fields. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 372(3), 1913-1983 [10.1090/tran/7699].

Finite dimensional invariant KAM tori for tame vector fields

CORSI, Livia;Feola, Roberto;Procesi, Michela
2019-01-01

Abstract

We discuss a Nash-Moser/KAM algorithm for the construction of invariant tori for tame vector fields. Similar algorithms have been studied widely both in finite and infinite dimensional contexts: we are particularly interested in the second case where tameness properties of the vector fields become very important. We focus on the formal aspects of the algorithm and particularly on the minimal hypotheses needed for convergence. We discuss various applications where we show how our algorithm allows one to reduce to solving only linear forced equations. We remark that our algorithm works at the same time in analytic and Sobolev classes.
Corsi, L., Feola, R., Procesi, M. (2019). Finite dimensional invariant KAM tori for tame vector fields. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 372(3), 1913-1983 [10.1090/tran/7699].
File in questo prodotto:
File Dimensione Formato  
CorsiFeolaProcesi_revised.pdf

accesso aperto

Descrizione: articolo
Tipologia: Documento in Post-print
Dimensione 890.25 kB
Formato Adobe PDF
890.25 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/353782
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 5
social impact