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Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points

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Abstract

In this article, we consider the entropy-expansiveness of geodesic flows on closed Riemannian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.

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Authors and Affiliations

  1. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, 266590, P. R. China

    Fei Liu

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China

    Fang Wang

  3. Beijing Center for Mathematics and Information Interdisciplinary Sciences (BCMIIS), Beijing, 100048, P. R. China

    Fang Wang

Authors
  1. Fei Liu
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  2. Fang Wang
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Correspondence to Fei Liu.

Additional information

The first author is supported by NSFC (Grant Nos. 11301305 and 11571207), and the grant “2012KYTD” from Shandong University of Science and Technology; the second author is supported by NSFC (Grant No. 11101294), Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20111108120001), and the grant of “Youxiu Rencai Peiyang Zizhu” (Class A) from the Beijing City

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Liu, F., Wang, F. Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points. Acta. Math. Sin.-English Ser. 32, 507–520 (2016). https://doi.org/10.1007/s10114-016-5200-5

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  • DOI: https://doi.org/10.1007/s10114-016-5200-5

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