On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori
Articolo
Data di Pubblicazione:
2020
Citazione:
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. [10.1016/j.cnsns.2020.105360]
Abstract:
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Hamiltonian normal forms; lower dimensional resonant tori; degenerate periodic orbits; linear stability
Elenco autori:
M. Sansottera, V. Danesi, T. Penati, S. Paleari
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