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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Finite dimensional invariant KAM tori for tame vector fields


Authors: Livia Corsi, Roberto Feola and Michela Procesi
Journal: Trans. Amer. Math. Soc. 372 (2019), 1913-1983
MSC (2010): Primary 37K55, 37J40
DOI: https://doi.org/10.1090/tran/7699
Published electronically: May 9, 2019
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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.


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Additional Information

Livia Corsi
Affiliation: Department of Mathematics, Emory University, Atlanta, Georgia 30307
Email: lcorsi@emory.edu

Roberto Feola
Affiliation: Dipartimento di Matematica, SISSA-Trieste, 34136 Trieste, Italy
Address at time of publication: Laboratoire de Mathématiques J. Leray, Université de Nantes, Nantes, France
Email: roberto.feola@univ-nantes.fr

Michela Procesi
Affiliation: Dipartimento di Matematica e Fisica, Università di Roma Tre, 00146 Roma RM, Italy
Email: procesi@mat.uniroma3.it

DOI: https://doi.org/10.1090/tran/7699
Received by editor(s): February 10, 2017
Received by editor(s) in revised form: June 13, 2018
Published electronically: May 9, 2019
Additional Notes: This research was supported by the European Research Council under FP7 “Hamiltonian PDEs and small divisor problems: a dynamical systems approach”, by PRIN2012 “Variational and perturbative aspects of non linear differential problems”, by the NSF grant DMS-1500943, and by McMaster University.
Article copyright: © Copyright 2019 American Mathematical Society