Multiplicity of polynomials on trajectories of polynomial vector fields in C3
Gabrielov, Andrei ; Jean, Frédéric ; Risler, Jean-Jacques
Banach Center Publications, Tome 43 (1998), p. 109-121 / Harvested from The Polish Digital Mathematics Library
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Let ξ be a polynomial vector field on n with coefficients of degree d and P be a polynomial of degree p. We are interested in bounding the multiplicity of a zero of a restriction of P to a non-singular trajectory of ξ, when P does not vanish identically on this trajectory. Bounds doubly exponential in terms of n are already known ([9,5,10]). In this paper, we prove that, when n=3, there is a bound of the form p+2p(p+d-1)2. In Control Theory, such a bound can be used to give an estimate of the degree of nonholonomy for a system of polynomial vector fields (this degree expresses the level of Lie-bracketing needed to generate the tangent space at each point).

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:208871 
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     author = {Gabrielov, Andrei and Jean, Fr\'ed\'eric and Risler, Jean-Jacques},
     title = {Multiplicity of polynomials on trajectories of polynomial vector fields in $C^3$
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     journal = {Banach Center Publications},
     volume = {43},
     year = {1998},
     pages = {109-121},
     zbl = {0922.32023},
     language = {en},
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Gabrielov, Andrei; Jean, Frédéric; Risler, Jean-Jacques. Multiplicity of polynomials on trajectories of polynomial vector fields in $C^3$
            . Banach Center Publications, Tome 43 (1998) pp. 109-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv44i1p109bwm/

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