Title:
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Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs
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Author:
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Giuliani, F.; Guardia, M.; Martin, P.; Pasquali, S.
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Abstract:
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The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on T2 exchanging energy among Fourier modes in a "chaotic-like" way. We say that a transition of energy is "chaotic-like" if either the choice of activated modes or the time spent in each transfer can be chosen randomly. We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations. The key point of the construction of the special solutions is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkho. Normal Form of those equations. © 2021 European Mathematical Society Publishing House. All rights reserved. |
Publication date:
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2021-04-23 |
Subject(s):
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Matemàtiques; Birkho. normal form; Hamiltonian PDEs; Transfer of energy |
Rights:
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L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by-nc-sa/4.0/ |
Pages:
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17 p. |
Document type:
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Article Article - Accepted version |
DOI:
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10.4171/RLM/931
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Published by:
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European Mathematical Society Publishing House
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Publish at:
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Rendiconti Lincei - Matematica e Applicazioni
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