Almost sure convergence of differentially positive systems on a globally orderable manifold
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913177125519360 |
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| author | Niu, Lin Wang, Yi Zhang, Yufeng |
| author_facet | Niu, Lin Wang, Yi Zhang, Yufeng |
| contents | Differentially positive systems are nonlinear systems whose linearization along trajectories preserves a cone field on a smooth Riemannian manifold. The structures of cone field come from general relativity and Lie theory. We prove that on a globally orderable manifold, the set of convergent points has full Riemann-Lebesgue measure, thus establishing almost sure convergence. This result thereby resolves a measure-theoretic form of the conjecture posed by Forni and Sepulchre in 2016 for such manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost sure convergence of differentially positive systems on a globally orderable manifold Niu, Lin Wang, Yi Zhang, Yufeng Dynamical Systems Differentially positive systems are nonlinear systems whose linearization along trajectories preserves a cone field on a smooth Riemannian manifold. The structures of cone field come from general relativity and Lie theory. We prove that on a globally orderable manifold, the set of convergent points has full Riemann-Lebesgue measure, thus establishing almost sure convergence. This result thereby resolves a measure-theoretic form of the conjecture posed by Forni and Sepulchre in 2016 for such manifolds. |
| title | Almost sure convergence of differentially positive systems on a globally orderable manifold |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2410.11895 |