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

• Volume: 4, page 137-158
• ISSN: 1292-8119

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## Abstract

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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 explicit. The complete list of local models in dimension 7 contains 13 items, and not 14, as written in[7], while the list in dimension 8 consists of 34 models (and not 41, as could be concluded from some statements in[7]). In these dimensions (and in lower dimensions, too) the models are eventually discerned just by their small growth vector at the origin.

## How to cite

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Cheaito, Mohamad, and Mormul, Piotr. "Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 137-158. <http://eudml.org/doc/197324>.

@article{Cheaito2010,
abstract = {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 explicit. The complete list of local models in dimension 7 contains 13 items, and not 14, as written in[7], while the list in dimension 8 consists of 34 models (and not 41, as could be concluded from some statements in[7]). In these dimensions (and in lower dimensions, too) the models are eventually discerned just by their small growth vector at the origin. },
author = {Cheaito, Mohamad, Mormul, Piotr},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Distribution; Goursat condition; flag; derived system; small growth vector.; distribution; small growth vector},
language = {eng},
month = {3},
pages = {137-158},
publisher = {EDP Sciences},
title = {Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8},
url = {http://eudml.org/doc/197324},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Mormul, Piotr
TI - Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 137
EP - 158
AB - 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 explicit. The complete list of local models in dimension 7 contains 13 items, and not 14, as written in[7], while the list in dimension 8 consists of 34 models (and not 41, as could be concluded from some statements in[7]). In these dimensions (and in lower dimensions, too) the models are eventually discerned just by their small growth vector at the origin.
LA - eng
KW - Distribution; Goursat condition; flag; derived system; small growth vector.; distribution; small growth vector
UR - http://eudml.org/doc/197324
ER -

## References

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11. P. Mormul, Local classification of rank -2 distributions satisfying the Goursat condition in dimension 9, preprint 582, Inst. of Math., Polish Acad. Sci., Warsaw, January (1998).
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