A Uniform Version of the Petrov-Khovanskii Theorem

Details A Uniform Version of the Petrov-Khovanskii Theorem A Uniform Version of the Petrov-Khovanskii Theorem

2011-08-09

arxiv.org/abs/1108.1846v1

Mathematics

Classical Analysis and ODEs

Scientific paper

An Abelian integral is the integral over the level curves of a Hamiltonian $H$ of an algebraic form $\omega$. The infinitesimal Hilbert sixteenth problem calls for the study of the number of zeros of Abelian integrals in terms of the degrees $H$ and $\omega$. Petrov and Khovanskii have shown that this number grows at most linearly with the degree of $\omega$, but gave a purely existential bound. Binyamini, Novikov and Yakovenko have given an \emph{explicit} bound growing doubly-exponentially with the degree. We combine the techniques used in the proofs of these two results, to obtain an explicit bound on the number of zeros of Abelian integrals growing linearly with $\deg\omega$.

Affiliated with

Also associated with

No associations

Rating

A Uniform Version of the Petrov-Khovanskii Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Uniform Version of the Petrov-Khovanskii Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Uniform Version of the Petrov-Khovanskii Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-69864