Prevalent behavior and almost sure Poincare-Bendixson Theorem for smooth flows with invariant k-cones
Dynamical Systems
2022-03-08 v2
Abstract
We investigate the global dynamics from a measure-theoretic perspective for smooth flows with invariant cones of rank k. For such systems, it is shown that prevalent (or equivalently, almost all) orbits will be pseudo-ordered or convergent to equilibria. This reduces to Hirsch's prevalent convergence Theorem if the rank k=1; and implies an almost-sure Poincare-Bendixson Theorem for the case k=2. These results are then applied to obtain an almost sure Poincare-Bendixson theorem for high-dimensional differential equations.
Keywords
Cite
@article{arxiv.2202.13128,
title = {Prevalent behavior and almost sure Poincare-Bendixson Theorem for smooth flows with invariant k-cones},
author = {Yi Wang and Jinxiang Yao and Yufeng Zhang},
journal= {arXiv preprint arXiv:2202.13128},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:1905.06787