When Jacobian matrices at two saddle-centers share the same pair of purely imaginary eigenvalues, transverse heteroclinic intersections on a common energy surface occur exactly under the paper's cited sufficient conditions for nonintegrability; otherwise intersections are independent of those条件.
Galoisian obstructions to non-Hamiltonian integrability
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abstract
We show that the main theorem of Morales--Ramis--Simo about Galoisian obstructions to meromorphic integrability of Hamiltonian systems can be naturally extended to the non-Hamiltonian case. Namely, if a dynamical system is meromorphically integrable in the non-Hamiltonian sense, then the differential Galois groups of the variational equations (of any order) along its solutions must be virtually Abelian
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math.DS 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Heteroclinic Orbits and Nonintegrability in Two-Degree-of-Freedom Hamiltonian Systems with Saddle-Centers
When Jacobian matrices at two saddle-centers share the same pair of purely imaginary eigenvalues, transverse heteroclinic intersections on a common energy surface occur exactly under the paper's cited sufficient conditions for nonintegrability; otherwise intersections are independent of those条件.