Chaotic-Like Transfers of Energy in Hamiltonian PDEs

We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on [Formula: see text] and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange can be considered “chaotic-like” since either t...

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Autores principales: Giuliani, Filippo, Guardia, Marcel, Martin, Pau, Pasquali, Stefano
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550714/
https://www.ncbi.nlm.nih.gov/pubmed/34720123
http://dx.doi.org/10.1007/s00220-021-03956-9
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author Giuliani, Filippo
Guardia, Marcel
Martin, Pau
Pasquali, Stefano
author_facet Giuliani, Filippo
Guardia, Marcel
Martin, Pau
Pasquali, Stefano
author_sort Giuliani, Filippo
collection PubMed
description We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on [Formula: see text] and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange can be considered “chaotic-like” since either the choice of activated modes or the time spent in each transfer can be chosen randomly. The key point of the construction of those orbits is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkhoff Normal Form truncation of those equations.
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spelling pubmed-85507142021-10-29 Chaotic-Like Transfers of Energy in Hamiltonian PDEs Giuliani, Filippo Guardia, Marcel Martin, Pau Pasquali, Stefano Commun Math Phys Article We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on [Formula: see text] and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange can be considered “chaotic-like” since either the choice of activated modes or the time spent in each transfer can be chosen randomly. The key point of the construction of those orbits is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkhoff Normal Form truncation of those equations. Springer Berlin Heidelberg 2021-02-08 2021 /pmc/articles/PMC8550714/ /pubmed/34720123 http://dx.doi.org/10.1007/s00220-021-03956-9 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Giuliani, Filippo
Guardia, Marcel
Martin, Pau
Pasquali, Stefano
Chaotic-Like Transfers of Energy in Hamiltonian PDEs
title Chaotic-Like Transfers of Energy in Hamiltonian PDEs
title_full Chaotic-Like Transfers of Energy in Hamiltonian PDEs
title_fullStr Chaotic-Like Transfers of Energy in Hamiltonian PDEs
title_full_unstemmed Chaotic-Like Transfers of Energy in Hamiltonian PDEs
title_short Chaotic-Like Transfers of Energy in Hamiltonian PDEs
title_sort chaotic-like transfers of energy in hamiltonian pdes
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550714/
https://www.ncbi.nlm.nih.gov/pubmed/34720123
http://dx.doi.org/10.1007/s00220-021-03956-9
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