vix.ing · top · new · best · stats · spec

Bifurcations of the polycycle "tears of the heart": multiple numerical\n invariants

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

Abstract

"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

Cited by

Related