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Dynamics on Networks of Manifolds
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Dynamics on Networks of Manifolds
Інший ID:
2010 Mathematics Subject Classification: 34C14; 18D99
DOI:10.3842/SIGMA.2015.022
DOI:10.3842/SIGMA.2015.022
Посилання:
Dynamics on Networks of Manifolds / L. DeVille, E. Lerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 12 назв. — англ.
Підтримка:
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.
Дата:
2015
Переглядів:
635
Завантажень:
271
Анотація:
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.
