On a Galoisian approach to the splitting of separatrices

DOI10.5802/afst.925zbMath0971.34076OpenAlexW2329728885MaRDI QIDQ1576401

Juan J. Morales-Ruiz, Josep Maria Peris

Publication date: 2 January 2001

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_1999_6_8_1_125_0

zbMATH Keywords

Hamiltonian systemshomoclinic orbitGalois differential approachLerman theoremZiglin nonintegrability theorem

Mathematics Subject Classification ID

Differential algebra (12H05) Abstract differential equations (12H20) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items

Differential Galois theory and Darboux transformations for integrable systems ⋮ Integrability of the Zakharov-Shabat systems by quadrature ⋮ Some questions looking for answers in dynamical systems ⋮ Integrability of Hamiltonian systems and differential Galois groups of higher variational equations ⋮ Non-integrability of some few body problems in two degrees of freedom ⋮ Picard-Vessiot theory and integrability ⋮ Two generator subgroups of \(\text{SL}(2,\mathbf C)\) and the hypergeometric, Riemann, and Lamé equations ⋮ Horseshoes and invariant tori in cosmological models with a coupled field and non-zero curvature ^* ⋮ Nonintegrability of dynamical systems with homo- and heteroclinic orbits ⋮ Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level ⋮ Detection of symmetric homoclinic orbits to saddle-centres in reversible systems ⋮ Analytic and algebraic conditions for bifurcations of homoclinic orbits I: Saddle equilibria ⋮ Non-integrability of Gross-Neveu systems ⋮ Heteroclinic orbits and nonintegrability in two-degree-of-freedom Hamiltonian systems with saddle-centers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• An algorithm for solving second order linear homogeneous differential equations
• Picard-Vessiot theory and Ziglin's theorem
• Nonintegrability of some Hamiltonian systems, scattering and analytic continuation
• Non-integrability criteria for Hamiltonians in the case of Lamé normal variational equations
• On the Determination of Ziglin Monodromy Groups
• A conjecture in the arithmetic theory of differential equations