Displaying similar documents to “Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8”

On the geometry of Goursat structures

William Pasillas-Lépine, Witold Respondek (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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A Goursat structure on a manifold of dimension n is a rank two distribution 𝒟 such that dim 𝒟 ( i ) = i + 2 , for 0 i n - 2 , where 𝒟 ( i ) denote the elements of the derived flag of 𝒟 , defined by 𝒟 ( 0 ) = 𝒟 and 𝒟 ( i + 1 ) = 𝒟 ( i ) + [ 𝒟 ( i ) , 𝒟 ( i ) ] . Goursat structures appeared first in the work of von Weber and Cartan, who have shown that on an open and dense subset they can be converted into the so-called Goursat normal form. Later, Goursat structures have been studied by Kumpera and Ruiz. In the paper, we introduce a new local invariant for Goursat structures,...

Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8

Mohamad Cheaito, Piotr Mormul (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the rank–2 distributions satisfying so-called Goursat condition (GC); that is to say, codimension–2 differential systems forming with their derived systems a flag. Firstly, we restate in a clear way the main result of[7] giving preliminary local forms of such systems. Secondly – and this is the main part of the paper – in dimension 7 and 8 we explain which constants in those local forms can be made 0, normalizing the remaining ones to 1. All constructed equivalences are...

Parallelisability conditions for differentiable three-webs

Alena Vanžurová (1995)

Archivum Mathematicum

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Our aim is to find conditions under which a 3-web on a smooth 2 n -dimensional manifold is locally equivalent with a web formed by three systems of parallel n -planes in R 2 n . We will present here a new approach to this “classical” problem using projectors onto the distributions of tangent subspaces to the leaves of foliations forming the web.

On determining unknown functions in differential systems, with an application to biological reactors

Éric Busvelle, Jean-Paul Gauthier (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function ϕ . We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or...