We consider the classical problem of the continuation of periodic orbits surviving to the breaking of invariant lower dimensional resonant tori in nearly integrable Hamiltonian systems. In particular we extend our previous results (presented in CNSNS, 61:198-224, 2018) for full dimensional resonant tori to lower dimensional ones. We develop a constructive normal form scheme that allows to identify and approximate the periodic orbits which continue to exist after the breaking of the resonant torus. A specific feature of our algorithm consists in the possibility of dealing with degenerate periodic orbits. Besides, under suitable hypothesis on the spectrum of the approximate periodic orbit, we obtain information on the linear stability of the periodic orbits feasible of continuation. A pedagogical example involving few degrees of freedom, but connected to the classical topic of discrete solitons in dNLS-lattices, is also provided.
On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori / M. Sansottera, V. Danesi, T. Penati, S. Paleari. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 90(2020 Nov), pp. 105360.1-105360.23.
Titolo: | On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori |
Autori: | |
Parole Chiave: | Hamiltonian normal forms; lower dimensional resonant tori; degenerate periodic orbits; linear stability |
Settore Scientifico Disciplinare: | Settore MAT/07 - Fisica Matematica |
Progetto: | New frontiers of Celestial Mechanics: theory and applications |
Data di pubblicazione: | nov-2020 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.cnsns.2020.105360 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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