Basins of Equilibria and geometry of Global Sectors in Holomorphic Flows
In this follow-up paper to [Local geometry of Equilibria and a Poincare-Bendixson-type Theorem for Holomorphic Flows, Nicolas Kainz, Dirk Lebiedz (2024)] we investigate the global topology and geometry of dynamical systems $\dot{x} = F(x)$ with entire vector field $F$ by exploiting and extending the...
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| creator | Kainz, Nicolas Lebiedz, Dirk |
| description | In this follow-up paper to [Local geometry of Equilibria and a
Poincare-Bendixson-type Theorem for Holomorphic Flows, Nicolas Kainz, Dirk
Lebiedz (2024)] we investigate the global topology and geometry of dynamical
systems $\dot{x} = F(x)$ with entire vector field $F$ by exploiting and
extending the local structure of finite elliptic decompositions. We prove
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 notion of a
sector-forming orbit allowing global topological analysis. The structure of
heteroclinic regions between two equilibria is characterized. |
| doi_str_mv | 10.48550/arxiv.2410.04895 |
| format | Article |
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Poincare-Bendixson-type Theorem for Holomorphic Flows, Nicolas Kainz, Dirk
Lebiedz (2024)] we investigate the global topology and geometry of dynamical
systems $\dot{x} = F(x)$ with entire vector field $F$ by exploiting and
extending the local structure of finite elliptic decompositions. We prove
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 notion of a
sector-forming orbit allowing global topological analysis. The structure of
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Poincare-Bendixson-type Theorem for Holomorphic Flows, Nicolas Kainz, Dirk
Lebiedz (2024)] we investigate the global topology and geometry of dynamical
systems $\dot{x} = F(x)$ with entire vector field $F$ by exploiting and
extending the local structure of finite elliptic decompositions. We prove
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 notion of a
sector-forming orbit allowing global topological analysis. The structure of
heteroclinic regions between two equilibria is characterized.</description><subject>Mathematics - Complex Variables</subject><subject>Mathematics - Dynamical Systems</subject><subject>Mathematics - Geometric Topology</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzMgEKGJhYWJpyMng4JRZn5hUr5KcpuBaWZuZkJhVlJiok5qUopKfm56aWFFWCpNxz8pMScxSCU5NL8ouKFTLzFDzyc_Jz84sKMjKTFdxy8suLeRhY0xJzilN5oTQ3g7yba4izhy7YzviCoszcxKLKeJDd8WC7jQmrAADFszlp</recordid><startdate>20241007</startdate><enddate>20241007</enddate><creator>Kainz, Nicolas</creator><creator>Lebiedz, Dirk</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20241007</creationdate><title>Basins of Equilibria and geometry of Global Sectors in Holomorphic Flows</title><author>Kainz, Nicolas ; Lebiedz, Dirk</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2410_048953</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Complex Variables</topic><topic>Mathematics - Dynamical Systems</topic><topic>Mathematics - Geometric Topology</topic><toplevel>online_resources</toplevel><creatorcontrib>Kainz, Nicolas</creatorcontrib><creatorcontrib>Lebiedz, Dirk</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kainz, Nicolas</au><au>Lebiedz, Dirk</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Basins of Equilibria and geometry of Global Sectors in Holomorphic Flows</atitle><date>2024-10-07</date><risdate>2024</risdate><abstract>In this follow-up paper to [Local geometry of Equilibria and a
Poincare-Bendixson-type Theorem for Holomorphic Flows, Nicolas Kainz, Dirk
Lebiedz (2024)] we investigate the global topology and geometry of dynamical
systems $\dot{x} = F(x)$ with entire vector field $F$ by exploiting and
extending the local structure of finite elliptic decompositions. We prove
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 notion of a
sector-forming orbit allowing global topological analysis. The structure of
heteroclinic regions between two equilibria is characterized.</abstract><doi>10.48550/arxiv.2410.04895</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Complex Variables Mathematics - Dynamical Systems Mathematics - Geometric Topology |
| title | Basins of Equilibria and geometry of Global Sectors in Holomorphic Flows |
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