Carregant...
Fitxers
Tipus de document
TesiVersió
Versió publicadaData de publicació
Llicència de publicació
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/206002
Degenerate invariant tori in KAM theory
Títol de la revista
Autors
Director/Tutor
ISSN de la revista
Títol del volum
Resum
[eng] The thesis develops an incipient methodology to study bifurcations of invariant curves in one-dimensional and quasiperiodic discrete systems, based on translated curve theorems and KAM theory.The (extended) phase space is a bundle whose base is a torus of dimension 1, and the real-line is the fiber but both the methodology and the results can be easily adapted to higher dimensional tori (the dimension being the number of external frequencies). The systems themselves are maps of bundles over translations in the torus with d frequencies. over translations on the torus with d frequencies. The methodology involves KAM theory, bifurcation theory, and translated curve theorems (in the spirit of Moser, Rüßmann, Herman, Delshams and Ortega). In the project, rigorous results are obtained in a posteriori format on the existence of families of translated tori in the analytical framework, establishing a methodology to study the bifurcations of translated tori. The a posteriori format is suitable to develop rigorous numerical calculations. Complementarily, the algorithms derived from the iterative process associated with this methodology have been implemented on the computer.
Descripció
Matèries (anglès)
Citació
Col·leccions
Citació
PELLO GARCÍA, Juan. Degenerate invariant tori in KAM theory. [consulta: 5 de desembre de 2025]. [Disponible a: https://hdl.handle.net/2445/206002]