Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs
(2021) In Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni 32(1). p.149-166- 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.
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- author
- Giuliani, Filippo ; Guardia, Marcel ; Martin, Pau and Pasquali, Stefano LU
- organization
- publishing date
- 2021-04
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Birkho. normal form, Hamiltonian PDEs, Transfer of energy
- in
- Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
- volume
- 32
- issue
- 1
- pages
- 18 pages
- publisher
- European Mathematical Society Publishing House
- external identifiers
-
- scopus:85106298226
- ISSN
- 1120-6330
- DOI
- 10.4171/RLM/931
- language
- English
- LU publication?
- yes
- id
- e979e65d-f692-44ca-ac5e-cc740f8ae9c6
- date added to LUP
- 2022-01-04 14:52:38
- date last changed
- 2022-04-27 07:00:50
@article{e979e65d-f692-44ca-ac5e-cc740f8ae9c6, abstract = {{<p>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.</p>}}, author = {{Giuliani, Filippo and Guardia, Marcel and Martin, Pau and Pasquali, Stefano}}, issn = {{1120-6330}}, keywords = {{Birkho. normal form; Hamiltonian PDEs; Transfer of energy}}, language = {{eng}}, number = {{1}}, pages = {{149--166}}, publisher = {{European Mathematical Society Publishing House}}, series = {{Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni}}, title = {{Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs}}, url = {{http://dx.doi.org/10.4171/RLM/931}}, doi = {{10.4171/RLM/931}}, volume = {{32}}, year = {{2021}}, }