Abstract
We study bi-Lyapunov stable homoclinic classes for a C1 generic flow on a closed Riemannian manifold and prove that such a homoclinic class contains no singularity. This enables a parallel study of bi-Lyapunov stable dynamics for flows and for diffeomorphisms. For example, we can then show that a bi-Lyapunov stable homoclinic class for a C1 generic flow is hyperbolic if and only if all periodic orbits in the class have the same stable index.
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The author thanks the referees very much for their precious time and valuable comments. The author thanks also the Shenzhen Postdoctoral Funding for its financial support.
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Zheng, R.S. Bi-Lyapunov Stable Homoclinic Classes for C1 Generic Flows. Acta. Math. Sin.-English Ser. 37, 1023–1040 (2021). https://doi.org/10.1007/s10114-021-0420-8
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DOI: https://doi.org/10.1007/s10114-021-0420-8