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2019-01-23  03:40 hrs.

Multiplicity of a polynomial on a trajectory of a polynomial vector field

Andrei Gabrielov
Purdue University

The problem of computing (or at least obtaining an upper bound for) the

multiplicity of a polynomial restricted to a trajectory of a polynomial

vector field has important applications in control theory and in analytic

number theory. The multivariable version of this problem is computing the

multiplicity of an isolated zero of a system of Noetherian functions

(restrictions of polynomials to integral manifolds of Pfaffian partial

differential equations). The multiplicity of such a zero can be expressed

in terms of the Euler characteristics of generalized Milnor fibers

associated with the system of equations. This provides an effective upper 

bound on the multiplicity. Recently, these results have been improved by 

G. Binyamini, and extended by G. Binyamini and D. Novikov to non-isolated 



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