DOI QR코드

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ROBUSTLY SHADOWABLE CHAIN COMPONENTS OF C1 VECTOR FIELDS

  • Lee, Keonhee (Department of Mathematics Chungnam National University) ;
  • Le, Huy Tien (Department of Mathematics Vietnam National University) ;
  • Wen, Xiao (The School of Mathematics and System Science Beihang University)
  • 투고 : 2012.08.13
  • 발행 : 2014.01.01

초록

Let ${\gamma}$ be a hyperbolic closed orbit of a $C^1$ vector field X on a compact boundaryless Riemannian manifold M, and let $C_X({\gamma})$ be the chain component of X which contains ${\gamma}$. We say that $C_X({\gamma})$ is $C^1$ robustly shadowable if there is a $C^1$ neighborhood $\mathcal{U}$ of X such that for any $Y{\in}\mathcal{U}$, $C_Y({\gamma}_Y)$ is shadowable for $Y_t$, where ${\gamma}_Y$ denotes the continuation of ${\gamma}$ with respect to Y. In this paper, we prove that any $C^1$ robustly shadowable chain component $C_X({\gamma})$ does not contain a hyperbolic singularity, and it is hyperbolic if $C_X({\gamma})$ has no non-hyperbolic singularity.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation (NRF)

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피인용 문헌

  1. SHADOWABLE CHAIN COMPONENTS AND HYPERBOLICITY vol.52, pp.1, 2015, https://doi.org/10.4134/BKMS.2015.52.1.149
  2. Weak measure expansive flows vol.260, pp.2, 2016, https://doi.org/10.1016/j.jde.2015.09.017
  3. HYPERBOLICITY OF HOMOCLINIC CLASSES OF VECTOR FIELDS vol.98, pp.03, 2015, https://doi.org/10.1017/S1446788714000640
  4. Robustly shadowable chain transitive sets and hyperbolicity vol.33, pp.4, 2018, https://doi.org/10.1080/14689367.2017.1417355