Families of vector fields with many numerical invariants Academic Article uri icon

abstract

  • We study bifurcations in finite-parameter families of vector fields on \begin{document}$S^2$end{document}. Recently, Yu. Ilyashenko, Yu. Kudryashov, and I. Schurov provided examples of (locally generic) structurally unstable \begin{document}$3$end{document}-parameter families of vector fields: topological classification of these families admits at least one numerical invariant. They also provided examples of \begin{document}$(2D+1)$end{document}-parameter families such that the topological classification of these families has at least \begin{document}$D$end{document} numerical invariants and used those examples to construct families with functional invariants of topological classification.

    In this paper, we construct locally generic \begin{document}$4$end{document}-parameter families with any prescribed number of numerical invariants and use them to construct \begin{document}$5$end{document}-parameter families with functional invariants. We also describe a locally generic class of \begin{document}$3$end{document}-parameter families with a tail of an infinite number sequence as an invariant of topological classification.

published proceedings

  • Discrete and Continuous Dynamical Systems

author list (cited authors)

  • Goncharuk, N., & Kudryashov, Y.

citation count

  • 0

complete list of authors

  • Goncharuk, Nataliya||Kudryashov, Yury

publication date

  • January 2022