arXiv:2405.04281 Abstract | arXiv Analytics

arXiv:2405.04281 [math.DS]Abstract References Reviews Resources

On a variant of Hilbert's 16th problem

Published 2024-05-07Version 1

We study the number of limit cycles that a planar polynomial vector field can have as a function of its number $m$ of monomials. We prove that the number of limit cycles increases at least quadratically with $m$ and we provide good lower bounds for $m\le10.$

Categories: math.DS

Keywords: hilberts 16th problem, planar polynomial vector field, limit cycles increases, lower bounds

Related articles: Most relevant | Search more

arXiv:2103.07193 [math.DS] (Published 2021-03-12)

Hilbert's 16th problem

Pablo Pedregal

arXiv:1110.2154 [math.DS] (Published 2011-10-10, updated 2015-04-25)

Comments about Hilbert's 16'th problem

John Atwell Moody

arXiv:1610.07582 [math.DS] (Published 2016-10-24)

Hilbert's 16th problem on a period annulus and Nash space of arcs

Jean-Pierre Françoise, Lubomir Gavrilov, Dongmei Xiao