Desingularization of a completely nonholonomic module of vector fields

Prelegent(ci)

Piotr Mormul

Afiliacja

Uniwersytet Warszawski

Termin

22 kwietnia 2016 10:15

Pokój

p. 5840

Tytuł w języku angielskim

after [Chitour-Jean-Long 2013]

Seminarium

Seminarium Zakładu Układów Dynamicznych

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A module of vector fields on an n-dimensional manifold is bracket generating, its nonholonomy degree r is, say, big in comparison to n (r >> n). Its desingularization is a regular distribution of the same rank living on a much much bigger manifold. (One lifts up module's generators one by one. Together they span a regular distribution having a unique small growth vector (sgrv). Meaning that the lifted generators behave freely in the Lie algebra sense up to length r, when they start to span the full tangent bundle of the lifted manifold.) For instance, a not regular rank 2 distribution having at the reference point the small growth vector [2,3,4,5,5,6] gets desingularized on a 23-dimensional manifold. The sgrv of its desingularization, one and the same at every point, is Lie-free up to length six: [2,3,5,8,14,23].

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Such desingularization plays a key role in a recent, important in the sub-Riemannian geometry, preprint by Hakavuori and Le Donne.

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