3 papers
math.DS2022
Prevalent behavior and almost sure Poincare-Bendixson Theorem for smooth flows with invariant k-cones
Yi Wang, Jinxiang Yao, Yufeng Zhang
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 equivalent…
math.DS2021
Sharpened dynamics alternative and its -robustness for strongly monotone discrete dynamical systems
Yi Wang, Jinxiang Yao
For strongly monotone dynamical systems, the dynamics alternative for smooth discrete-time systems turns out to be a perfect analogy of the celebrated Hirsch's limit-set dichotomy…
math.DS2021
Prevalent Behavior of Smooth Strongly Monotone Discrete-Time Dynamical Systems
Yi Wang, Jinxiang Yao, Yufeng Zhang
For C1-smooth strongly monotone discrete-time dynamical systems, it is shown that ``convergence to linearly stable cycles" is a prevalent asymptotic behavior in the measuretheoreti…