Dynamics on Networks of Manifolds
We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently sur...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147001 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Dynamics on Networks of Manifolds / L. DeVille, E. Lerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862647112535113728 |
|---|---|
| author | DeVille, L. Lerman, E. |
| author_facet | DeVille, L. Lerman, E. |
| citation_txt | Dynamics on Networks of Manifolds / L. DeVille, E. Lerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give rise to projections of dynamical systems.
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| first_indexed | 2025-12-01T12:02:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147001 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T12:02:45Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | DeVille, L. Lerman, E. 2019-02-12T18:15:22Z 2019-02-12T18:15:22Z 2015 Dynamics on Networks of Manifolds / L. DeVille, E. Lerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34C14; 18D99 DOI:10.3842/SIGMA.2015.022 https://nasplib.isofts.kiev.ua/handle/123456789/147001 We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give rise to projections of dynamical systems. L.D. was supported by the National Science Foundation under grants CMG-0934491 and UBM1129198
 and by the National Aeronautics and Space Administration under grant NASA-NNA13
 AA91A. The authors also thank the anonymous referees whose comments significantly improved
 the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dynamics on Networks of Manifolds Article published earlier |
| spellingShingle | Dynamics on Networks of Manifolds DeVille, L. Lerman, E. |
| title | Dynamics on Networks of Manifolds |
| title_full | Dynamics on Networks of Manifolds |
| title_fullStr | Dynamics on Networks of Manifolds |
| title_full_unstemmed | Dynamics on Networks of Manifolds |
| title_short | Dynamics on Networks of Manifolds |
| title_sort | dynamics on networks of manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147001 |
| work_keys_str_mv | AT devillel dynamicsonnetworksofmanifolds AT lermane dynamicsonnetworksofmanifolds |