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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

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topCheaito, 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 - Cheaito, Mohamad

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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