caa a22 4500 606166416 CHVBK 20210128100658.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10440-014-9998-5 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9998-5 Verhulst Ferdinand Department of Mathematics, Utrecht University, P.O. Box 80.010, 3508, TA Utrecht, The Netherlands aut Integrability and Non-integrability of Hamiltonian Normal Forms [Elektronische Daten] [Ferdinand Verhulst] 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. Springer Science+Business Media Dordrecht, 2014 Hamiltonian systems nationallicence Normal forms nationallicence Non-integrability nationallicence Hamiltonian chains nationallicence Time-series nationallicence Acta Applicandae Mathematicae Springer Netherlands 137/1(2015-06-01), 253-272 0167-8019 137:1<253 2015 137 10440 https://doi.org/10.1007/s10440-014-9998-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9998-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Verhulst Ferdinand Department of Mathematics, Utrecht University, P.O. Box 80.010, 3508, TA Utrecht, The Netherlands aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 137/1(2015-06-01), 253-272 0167-8019 137:1<253 2015 137 10440