Non-integrability of the Armbruster-Guckenheimer-Kim quartic Hamiltonian through Morales-Ramis theory

2017/09/30 by P. Acosta-Humánez, Primitivo B. Acosta-Humánez, Acosta-Humánez, P. +5 · 2 citations
Mathematics · Physics and Astronomy · #12H05 #37J30 #70H06 #Advanced Algebra and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Hamiltonian (control theory) #Hamiltonian system #Integrable system #Mathematical optimization #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quartic function #math.DS #msc:12H05 #msc:37J30 #msc:70H06

paper · pdf · doi:10.48550/arxiv.1710.00227

Accepted for publication in SIAM Journal on Applied Dynamical Systems. Adapted version for arxiv with 19 pages and 11 figures

arxiv created 2017/09/30 · openalex publication_date 2017/09/30 · arxiv updated 2017/10/03 · openalex created_date 2017/10/20 · openalex updated_date 2026/08/06

Abstract

We show the non-integrability of the three-parameter Armburster-Guckenheimer-Kim quartic Hamiltonian using Morales-Ramis theory, with the exception of the three already known integrable cases. We use Poincaré sections to illustrate the breakdown of regular motion for some parameter values.

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