1. Non-uniformly hyperbolic flows and shadowing.
- Author
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Sun, Wenxiang, Tian, Xueting, and Vargas, Edson
- Subjects
- *
NON-uniform flows (Fluid dynamics) , *HYPERBOLIC functions , *SHADOWING theorem (Mathematics) , *ERGODIC theory , *COMPACTIFICATION (Mathematics) , *MANIFOLDS (Mathematics) - Abstract
We consider a hyperbolic ergodic measure of a C 1 flow on a compact manifold. Under the hypothesis that there are no fixed points and that the Oseledec splitting of the normal bundle satisfies a limit domination property, we prove that the measure has a shadowing property. As an application of this result we prove that the measure can be approached on the weak ⁎ topology by measures supported on hyperbolic periodic orbits. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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