Generic behavior of differentially positive systems on a globally orderable Riemannian manifold
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912758590603264 |
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| author | Niu, Lin Wang, Yi |
| author_facet | Niu, Lin Wang, Yi |
| contents | Differentially positive systems are the nonlinear systems whose linearization along trajectories preserves a cone field on a smooth Riemannian manifold. One of the embryonic forms for cone fields in reality is originated from the general relativity. By utilizing the Perron-Frobenius vector fields and the $Γ$-invariance of cone fields, we show that generic (i.e.,``almost all" in the topological sense) orbits are convergent to certain single equilibrium. This solved a reduced version of Forni-Sepulchre's conjecture in 2016 for globally orderable manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generic behavior of differentially positive systems on a globally orderable Riemannian manifold Niu, Lin Wang, Yi Dynamical Systems Differentially positive systems are the nonlinear systems whose linearization along trajectories preserves a cone field on a smooth Riemannian manifold. One of the embryonic forms for cone fields in reality is originated from the general relativity. By utilizing the Perron-Frobenius vector fields and the $Γ$-invariance of cone fields, we show that generic (i.e.,``almost all" in the topological sense) orbits are convergent to certain single equilibrium. This solved a reduced version of Forni-Sepulchre's conjecture in 2016 for globally orderable manifolds. |
| title | Generic behavior of differentially positive systems on a globally orderable Riemannian manifold |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2405.11434 |