Dynamics of mechanical systems with polynomial potentials

DOI10.1007/S10884-014-9357-2zbMath1404.37067OpenAlexW2017119446MaRDI QIDQ481266

Ernesto A. Lacomba, Manuel J. Falconi, Claudio Vidal

Publication date: 12 December 2014

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-014-9357-2

zbMATH Keywords

global flowHamiltonian vector fieldshomogeneous polynomial potentials

Mathematics Subject Classification ID

Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Asymptotic properties of solutions to ordinary differential equations (34D05)

Cites Work

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• On the dynamics of mechanical systems with the homogeneous polynomial potential \(V = ax ^{4} + cx ^{2} y ^{2}\)
• The flow of classical mechanical cubic potential systems
• Global dynamics of mechanical systems with cubic potentials
• A new necessary condition for the integrability of Hamiltonian systems with a two-dimensional homogeneous potential
• A mapping for the study of the 1/1 resonance in a galactic type Hamiltonian
• All meromorphically integrable 2D Hamiltonian systems with homogeneous potential of degree 3
• Pathology of invariant sets in the monkey saddle
• On the dynamics of mechanical systems with homogeneous polynomial potentials of degree \(4\)
• Geometry of the bifurcations of the normalized reduced Henon–Heiles family
• Chaos in a quartic dynamical model
• Differential Galois theory and non-integrability of Hamiltonian systems

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