Chaotic-like transfers of energy in hamiltonian PDEs
We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on T2 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 acti...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/363923 |
| Acceso en línea: | https://hdl.handle.net/2117/363923 https://dx.doi.org/10.1007/s00220-021-03956-9 |
| Access Level: | acceso abierto |
| Palabra clave: | Hamilton-Jacobi, Équations de Hamiltonian operator Equacions de Hamilton-Jacobi Hamiltonià (Operador matemàtic) Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on T2 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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