A line-bundle approach to contact integrability unifies cooriented and non-cooriented systems and covers dissipative contact Hamiltonians.
Solvability of a Lie algebra of vector fields implies their integrability by quadratures
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abstract
We present a substantial generalisation of a classical result by Lie on integrability by quadratures. Namely, we prove that all vector fields in a finite-dimensional transitive and solvable Lie algebra of vector fields on a manifold can be integrated by quadratures.
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Contact line bundles, foliations, and integrability
A line-bundle approach to contact integrability unifies cooriented and non-cooriented systems and covers dissipative contact Hamiltonians.