Diophantine "Tears of the Heart"
By: Yulij Ilyashenko, Stanislav Minkov, Ivan Shilin
Published: 2026-03-09
View on arXiv →#math.DS
Abstract
This paper studies topologically generic unfoldings of vector fields featuring a "tears of the heart" polycycle. It contrasts topological classification results with a metrical perspective, demonstrating that for most coefficient values, fewer invariants appear than previously thought. This has implications for understanding the stability and behavior of complex dynamical systems.