Abstract
In this paper, we consider weak horseshoe with bounded-gap-hitting times. For a flow \((M,\phi )\), it is shown that if the time one map \((M,\phi _1)\) has weak horseshoe with bounded-gap-hitting times, so is \((M,\phi _\tau )\) for all \(\tau \ne 0\). In addition, we prove that for an affine homeomorphism of a compact metric abelian group, positive topological entropy is equivalent to weak horseshoe with bounded-gap-hitting times.
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Acknowledgements
Leiye Xu is partially supported by NNSF of China (11801538, 11871188) and the USTC Research Funds of the Double First-Class Initiative. Junren Zheng is partially supported by NNSF of China (11971455). The authors would like to thank Wen Huang and Xiao Ma for making many valuable suggestions.
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Xu, L., Zheng, J. Weak Horseshoe with Bounded-Gap-Hitting Times. Commun. Math. Stat. 8, 463–472 (2020). https://doi.org/10.1007/s40304-020-00209-4
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DOI: https://doi.org/10.1007/s40304-020-00209-4