Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs

doi:10.4171/RLM/931

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RECERCAT Home > Centres de Recerca de Catalunya (CERCA) > Centre de Recerca Matemàtica > Articles > View document

Use this identifier to quote or link this document: http://hdl.handle.net/2072/531282

dc.contributor.author	Giuliani, F.
dc.contributor.author	Guardia, M.
dc.contributor.author	Martin, P.
dc.contributor.author	Pasquali, S.
dc.date.accessioned	2023-02-22T09:55:19Z
dc.date.available	2023-02-22T09:55:19Z
dc.date.issued	2021-04-23
dc.identifier.uri	http://hdl.handle.net/2072/531282
dc.description.sponsorship	PGC2018-100928-B-I00; Horizon 2020 Framework Programme, H2020: 757802; Ministerio de Ciencia, Innovación y Universidades, MCIU; European Research Council, ERC; Ministerio de Economía y Competitividad, MINECO; Institució Catalana de Recerca i Estudis Avançats, ICREA: 2017SGR1049; European Regional Development Fund, ERDF: PGC2018-098676-B-100
dc.format.extent	17 p.
dc.language.iso	eng
dc.publisher	European Mathematical Society Publishing House
dc.relation.ispartof	Rendiconti Lincei - Matematica e Applicazioni
dc.rights	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/
dc.source	RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other	Matemàtiques; Birkho. normal form; Hamiltonian PDEs; Transfer of energy
dc.title	Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs
dc.type	info:eu-repo/semantics/article
dc.type	info:eu-repo/semantics/acceptedVersion
dc.embargo.terms	cap
dc.relation.projectID	info:eu-repo/grantAgreement/EC/H2020/757802
dc.identifier.doi	10.4171/RLM/931
dc.rights.accessLevel	info:eu-repo/semantics/openAccess
dc.description.abstract	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.

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