Extension aux cycles singuliers du theoreme de Khovanski-Varchenko

Details Extension aux cycles singuliers du theoreme de Khovanski-Varchenko Extension aux cycles singuliers du theoreme de Khovanski-Varchenko

2009-12-07

arxiv.org/abs/0912.1354v1

Mathematics

Dynamical Systems

19 pages

Scientific paper

Let dH be a Hamiltonian one form on the real plane, of degre d. We show that,
if H is a Morse function, generic at infinity, then there exists a number N(d)
depending only on d, such that every small perturbation of dH has at most N(d)
limit cycles on the hole real plane, assuming that it's of degre at most d, and
that it has a non vanishing Abelian integral along real cycles of dH.

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