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- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Springer Science+Business Media Dordrecht
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-014-9998-5
- Publisher site
- See Article on Publisher Site
Abstract
This paper summarizes the present state of integrability of Hamiltonian normal forms and it aims at characterizing non-integrable behaviour in higher-dimensional systems. Non-generic behaviour in Hamiltonian systems can be a sign of integrability, but it is not a conclusive indication. We will discuss a few degenerations and briefly review the integrability of Hamiltonian normal forms in two and three degrees of freedom. In addition we discuss two integrable normal form Hamiltonian chains, FPU and 1:2:2:2:2:2, and three non-integrable normal form chains, with emphasis on the 1:2:3:3:3:3 resonance. To distinguish between various forms of non-integrability is a major issue; time-series and projections based on the presence of a universal quadratic integral of the normal forms can be a useful predictor.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 11, 2014