Snakes and articulated arms in an Hilbert space

Fernand Pelletier; Rebhia Saffidine

Annales de la faculté des sciences de Toulouse Mathématiques (2013)

  • Volume: 22, Issue: 3, page 525-557
  • ISSN: 0240-2963

Abstract

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The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional Hilbert space.

How to cite

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Pelletier, Fernand, and Saffidine, Rebhia. "Snakes and articulated arms in an Hilbert space." Annales de la faculté des sciences de Toulouse Mathématiques 22.3 (2013): 525-557. <http://eudml.org/doc/275330>.

@article{Pelletier2013,
abstract = {The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional Hilbert space.},
author = {Pelletier, Fernand, Saffidine, Rebhia},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {snakes; articulated arms; curves in Hilbert spaces; infinite-dimensional distributions; integrability of distributions},
language = {eng},
month = {6},
number = {3},
pages = {525-557},
publisher = {Université Paul Sabatier, Toulouse},
title = {Snakes and articulated arms in an Hilbert space},
url = {http://eudml.org/doc/275330},
volume = {22},
year = {2013},
}

TY - JOUR
AU - Pelletier, Fernand
AU - Saffidine, Rebhia
TI - Snakes and articulated arms in an Hilbert space
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2013/6//
PB - Université Paul Sabatier, Toulouse
VL - 22
IS - 3
SP - 525
EP - 557
AB - The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional Hilbert space.
LA - eng
KW - snakes; articulated arms; curves in Hilbert spaces; infinite-dimensional distributions; integrability of distributions
UR - http://eudml.org/doc/275330
ER -

References

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  1. Cabau (P.), Pelletier (F.).— Almost Lie algebroid structure on an anchored Banach bundle, Journal of Geometry and Physics Vol 62, p. 2147-2169 (2012). Zbl1262.53077MR2964651
  2. Dieudonné (J.).— Fondements de l’analyse moderne, Cahiers scientifiques Fasc XXVII, Gauthier-Villars, Paris (1967). Zbl0114.26602MR161945
  3. Hausmann (J.-C.).— Contrôle des bras articulés et transformations de Moëbus, Enseignement Mathématique, t. 51, p. 87-115 (2005). Zbl1171.70303MR2154622
  4. Lathuille (A.), Pelletier (F.).— On Sussmann theorem for orbits of set of vector fields on Banach manifolds, Bulletin des Sciences Mathématiques Vol 136, p. 579-616 (2012). Zbl1252.58003MR2944371
  5. Pelletier (F.).— Integrability of weak distributions on Banach manifolds, Indagationes Mathematicae 23, p. 214-242 (2012). Zbl1286.46087MR2948622
  6. Rodriguez (E.).— L’algorithme du charmeur de serpents, PhD Thesis, University of Geneva, http://www.unige.ch/cyberdocuments/theses2006/RodriguezE/these.pdf. 
  7. Sussmann (H.-J.).— Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc., vol 80, p. 171-188 (1973). Zbl0274.58002MR321133

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