1. Maximal tori in infinite-dimensional Hamiltonian systems: a Renormalization Group approach
- Author
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Corsi, Livia, Gentile, Guido, and Procesi, Michela
- Subjects
Mathematics - Dynamical Systems ,37K55, 37K06 - Abstract
We study the existence of infinite-dimensional invariant tori in a mechanical system of infinitely many rotators weakly interacting with each other. We consider explicitly interactions depending only on the angles, with the aim of discussing in a simple case the analyticity properties to be required on the perturbation of the integrable system in order to ensure the persistence of a large measure set of invariant tori with finite energy. The proof we provide of the persistence of the invariant tori implements the Renormalization Group scheme based on the tree formalism -- i.e. the graphical representation of the solutions of the equations of motion in terms of trees -- which has been widely used in finite-dimensional problems. The method is very effectual and flexible: it naturally extends, once the functional setting has been fixed, to the infinite-dimensional case with only minor technical-natured adaptations., Comment: 41 pages, 26 figures
- Published
- 2024