2018/08/22 by Nataliya Goncharuk, Goncharuk, Nataliya, Yury Kudryashov +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #34C23 #37E35 #37G99 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1808.07459
openalex publication_date 2018/08/22 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
"Tears of the heart" is a hyperbolic polycycle formed by three separatrix\nconnections of two saddles. It is met in generic 3-parameter families of planar\nvector fields.\n In [arXiv:1506.06797], it was discovered that generically, the bifurcation of\na vector field with "tears of the heart" is structurally unstable. The authors\nproved that the classification of such bifurcations has a numerical invariant.\n In this article, we study the bifurcations of "tears of the heart" in more\ndetail, and find out that the classification of such bifurcation may have\narbitrarily many numerical invariants.\n