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arXiv · 2405.11434

Generic behavior of differentially positive systems on a globally orderable Riemannian manifold

Lin Niu·Yi Wang
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Abstract

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 $\Gamma$-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.

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Lin Niu, Yi Wang. 2024-05-19. Generic behavior of differentially positive systems on a globally orderable Riemannian manifold. https://doi.org/10.1007/s00208-025-03203-9

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