Asymptotic motions converging to arbitrary dynamics for time-dependent Hamiltonians
Dynamical systems subject to perturbations that decay over time are relevant in the description of many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, as well as in celestial mechanics. For this reason, we consider a Hamiltonian dynamica...
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| Format: | article |
| Publication Date: | 2024 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/405417 |
| Online Access: | https://hdl.handle.net/2117/405417 https://dx.doi.org/10.1016/j.na.2024.113528 |
| Access Level: | Open access |
| Keyword: | Hamiltonian systems Dynamical systems KAM tori Time-dependence Sistemes hamiltonians Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Summary: | Dynamical systems subject to perturbations that decay over time are relevant in the description of many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, as well as in celestial mechanics. For this reason, we consider a Hamiltonian dynamical system having an invariant torus supporting arbitrary dynamics, and we study its evolution under a perturbation decaying exponentially over time. By applying a strategy based on a refined analysis of the Banach spaces and functionals involved in the resolution of suitable non-linear invariant equations, we show the existence of orbits converging in time to the arbitrary motions associated with the unperturbed system. As a corollary, an analogous statement for time-dependent vector fields on the torus is also obtained. This result extends to the important case of arbitrary Hamiltonian dynamics a previous work of Canadell and de la Llave where only asymptotic quasi-periodic motions were considered. |
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