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Hierarchies of cofactor systems. (English) Zbl 1040.37044

Summary: We assign to any cofactor system a whole hierarchy of such systems. A sufficient condition for their complete integrability is given. The hierarchies admit construction of nontrivial integrable systems from trivial ones.

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
53D25 Geodesic flows in symplectic geometry and contact geometry
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70H03 Lagrange’s equations
70H05 Hamilton’s equations
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