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arXiv · 2410.11895

Almost sure convergence of differentially positive systems on a globally orderable manifold

Lin Niu·Yi Wang·Yufeng Zhang
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Abstract

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.

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Lin Niu, Yi Wang, Yufeng Zhang. 2024-10-14. Almost sure convergence of differentially positive systems on a globally orderable manifold. https://arxiv.org/abs/2410.11895

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