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Local convexity for second order differential equations on a Lie algebroid. (English) Zbl 1477.34028

Summary: A theory of local convexity for a second order differential equation (sode) on a Lie algebroid is developed. The particular case when the (sode) is homogeneous quadratic is extensively discussed.

MSC:

34A26 Geometric methods in ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
17B66 Lie algebras of vector fields and related (super) algebras
22A22 Topological groupoids (including differentiable and Lie groupoids)
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