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Restricted version of the infinitesimal Hilbert 16th problem

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Abstract

The paper deals with an abelian integral of a polynomial 1- form along a family of real ovals of a polynomial (hamiltonian) in two variables (the integral is considered as a function of value of the hamiltonian). We give an explicit upper bound of the number of its zeros (assuming the hamiltonian ultra-Morse of arbitrary degree and ranging in a compact subset in the space of ultra-Morse polynomials of a given degree, and that the form has a smaller degree). This bound depends on the choice of the compact set and is exponential in the fourth power of the degree.
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Dates and versions

ensl-00078858 , version 1 (07-06-2006)

Identifiers

  • HAL Id : ensl-00078858 , version 1

Cite

Alexey Glutsyuk, Yuli Ilyashenko. Restricted version of the infinitesimal Hilbert 16th problem. 2006. ⟨ensl-00078858⟩
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