PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert's 16th problem.
This paper is a part of the program to prove the finiteness part of Hilbert's 16th problem for quadratic systems which consists in proving that 121~graphics of such systems have finite cyclicity. The authors show that any pp-graphic through a multiplicity~3 nilpotent singularity of elliptic type which does not surround a center has finite cyclicity. Altogether, the authors show the finite cyclicity of 15~graphics. In particular, they prove the finite cyclicity of a pp-graphic with a nilpotent elliptic singular point together with a hyperbolic saddle with hyperbolicity different from~1 which appears in generic 3-parameter families of vector fields and hence belongs to the ``zoo'' of Kotova and Stanzo.
scientific article; zbMATH DE number 2033006
scientific article