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Relative generic singularities of the exponential map. (English) Zbl 0836.58034
Authors’ abstract: “The authors investigate generic properties of the exponential map defined as $$\text{Exp}(v)= h^v_1$$, for a vector field $$v\in \Gamma(g)$$ (where $$\Gamma(g)$$ denotes the Lipschitz sections of a subset $$g$$ of vector subspaces of the sheaf of all smooth vector fields on a smooth manifold $$M$$ and $$h^v_t$$ is the flow generated by $$v$$).
They study restrictions of Exp to a suitable class of germs of submanifolds of $$M$$, and find necessary and sufficient conditions for a subsheaf $$h\subset z$$ such that for a generic vector field $$v\in \Gamma(h)$$ the singularities of the flow of $$v$$ arise as singularities of the flow of a generic vector field belonging to $$\Gamma(g)$$. Applications of these results to Riemannian and sub-Riemannian geometry are presented and the context is chosen to include a theorem of A. Weinstein concerning the Riemannian exponential map”.

##### MSC:
 37C10 Dynamics induced by flows and semiflows
Full Text:
##### References:
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