Basins of Equilibria and geometry of Global Sectors in Holomorphic Flows
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915479640080384 |
|---|---|
| author | Kainz, Nicolas Lebiedz, Dirk |
| author_facet | Kainz, Nicolas Lebiedz, Dirk |
| contents | In this follow-up paper, we investigate the global geometry and topology of dynamical systems $\dot{x} = F(x)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Basins of Equilibria and geometry of Global Sectors in Holomorphic Flows Kainz, Nicolas Lebiedz, Dirk Dynamical Systems Complex Variables Geometric Topology 30A99, 30C10, 30C15, 30D30 (Primary), 32M25, 37F10, 37F75 (Secondary) In this follow-up paper, we investigate the global geometry and topology of dynamical systems $\dot{x} = F(x)$ 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. |
| title | Basins of Equilibria and geometry of Global Sectors in Holomorphic Flows |
| topic | Dynamical Systems Complex Variables Geometric Topology 30A99, 30C10, 30C15, 30D30 (Primary), 32M25, 37F10, 37F75 (Secondary) |
| url | https://arxiv.org/abs/2410.04895 |