Families of vector fields with many numerical invariants
Dynamical Systems
2023-12-19 v2
Abstract
We study bifurcations in finite-parameter families of vector fields on . Recent papers by Yu. Ilyashenko, N. Goncharuk, Yu. Kudryashov, I. Schurov, and N. Solodovnikov provide examples of (locally generic) structurally unstable families of 3-parameter vector fields: generic close 3-parameter families experience different bifurcations. In this paper, we use these results to construct new examples of few-parameter generic families of planar vector fields such that their classification has many invariants. In particular, we construct (a) 3-parameter families with infinitely many numerical invariants; (b) 4-parameter families with arbitrarily many "robust" numerical invariants; (c) 5-parameter families with functional invariants.
Keywords
Cite
@article{arxiv.2003.01269,
title = {Families of vector fields with many numerical invariants},
author = {Nataliya Goncharuk and Yury Kudryashov},
journal= {arXiv preprint arXiv:2003.01269},
year = {2023}
}