2024/10/07 by Nicolas Kainz, Kainz, Nicolas, Dirk Lebiedz +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #30A99 #30C10 #30C15 #30D30 (Primary) #32M25 #37F10 #37F75 (Secondary) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #Economic theories and models #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2410.04895
openalex publication_date 2024/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this follow-up paper, we investigate the global geometry and topology of dynamical systems x = F(x) with entire vector field F, building on and constructively extending the local structure of simple and higher-order equilibria. We provide a step-by-step analysis to reveal topological properties of the basins of centers, nodes, and foci, while excluding isolated equilibria at the boundaries of the latter two. We propose a definition of global elliptic sectors and introduce the concept of sector-forming orbits based on the geometry within a finite elliptic decomposition of multiple equilibria. Finally, we characterize the structure of heteroclinic regions connecting two equilibria.