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Shadowing, expansiveness and stability of divergence-free vector fields

Celia Ferreira
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회보 (Bulletin of the KMS)|제51권 제1호|pp. 67-76

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참고문헌

키워드

shadowingexpansivenessLipschitz shadowingAnosov vector fields
주제분류수학

초록

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: • X is a divergence-free vector field satisfying the shadowing property. • X is a divergence-free vector field satisfying the Lipschitz shadowing property. • X is an expansive divergence-free vector field. • X has no singularities and is Anosov.

Abstract

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: • X is a divergence-free vector field satisfying the shadowing property. • X is a divergence-free vector field satisfying the Lipschitz shadowing property. • X is an expansive divergence-free vector field. • X has no singularities and is Anosov.

참고문헌 (19)

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  14. S. Pilyugin, "Lecture Notes Math." (1999), Springe
  15. S. Pilyugin, "Lipschitz shadowing implies structural stability", Nonlinearity, 23(10), pp.2509~2515 (2010)
  16. S. Smale, "Differentiable dynamical systems", Bull. Amer. Math. Soc, 73, pp.747~817 (1967)
  17. S. Tikhomirov, "Interiors of sets of vector fields with shadowing corresponding to certain classes of reparameterizations", Vestnik St. Petersburg Univ. Math, 41(4), pp.360~366 (2008)
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