Galoisian obstructions to integrability and Melnikov criteria for chaos in two-degree-of-freedom Hamiltonian systems with saddle centres

DOI10.1088/0951-7715/16/6/307zbMath1070.37038OpenAlexW2023802108MaRDI QIDQ4444056

Publication date: 10 March 2004

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/16/6/307

zbMATH Keywords

chaos differential Galois approach Melnikov type approach nonintegrability Hamiltonian systems pendulum-oscillator type Hamiltonian

Mathematics Subject Classification ID

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (11)

On first integrals of a family of generalized Lorenz-like systems ⋮ Integrability of the Zakharov-Shabat systems by quadrature ⋮ Integrability of Hamiltonian systems and differential Galois groups of higher variational equations ⋮ Galoisian obstruction to the integrability of general dynamical systems ⋮ Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application ⋮ Non-integrability of some few body problems in two degrees of freedom ⋮ Horseshoes and invariant tori in cosmological models with a coupled field and non-zero curvature ^* ⋮ Nonintegrability of dynamical systems with homo- and heteroclinic orbits ⋮ Detection of symmetric homoclinic orbits to saddle-centres in reversible systems ⋮ Analytic and algebraic conditions for bifurcations of homoclinic orbits I: Saddle equilibria ⋮ Heteroclinic orbits and nonintegrability in two-degree-of-freedom Hamiltonian systems with saddle-centers

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