Note on integrability of certain homogeneous Hamiltonian systems

DOI10.1016/j.physleta.2015.08.032zbMath1349.37058arXiv1606.03023OpenAlexW1933091254WikidataQ104404661 ScholiaQ104404661MaRDI QIDQ341431

Maria Przybylska, Wojciech Szumiński, Andrzej J. Maciejewski

Publication date: 16 November 2016

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.03023

zbMATH Keywords

differential Galois theoryLiouville integrabilityintegrability obstructionssystems in curved spacessystems in polar coordinates

Mathematics Subject Classification ID

Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

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Cites Work

• Unnamed Item
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• A note on the non-integrability of some Hamiltonian systems with a homogeneous potential.
• A note on algebraic potentials and Morales-Ramis theory
• A necessary condition for the integrability of homogeneous Hamiltonian systems with two degrees of freedom
• Second Order Differential Equations
• Differential Galois theory and non-integrability of Hamiltonian systems