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arXiv · 2202.09742

Lyapunov stable chain recurrence classes for singular flows

Shaobo Gan·Jiagang Yang·Rusong Zheng
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Abstract

We show that for a $C^1$ generic vector field $X$ away from homoclinic tangencies, a nontrivial Lyapunov stable chain recurrence class is a homoclinic class. The proof uses an argument with $C^2$ vector fields approaching $X$ in $C^1$ topology, with their Gibbs $F$-states converging to a Gibbs $F$-state of $X$.

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Shaobo Gan, Jiagang Yang, Rusong Zheng. 2022-02-20. Lyapunov stable chain recurrence classes for singular flows. https://arxiv.org/abs/2202.09742

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