In this paper, we introduce the notion of the asymptotic orbital pseudo-orbit tracing property for a vector field X of a compact smooth manifold M. We show that if a vector field X has the \(C^1\) robust asymptotic orbital pseudo-orbit tracing property, then it is Anosov, and if a \(C^1\) generic vector field X has the asymptotic orbital pseudo-orbit tracing property, then it is Anosov. Moreover, we also show our results for divergence-free vector fields and Hamiltonian systems.

中文翻译：

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具有渐近轨道伪轨道跟踪特性的矢量场

在本文中，我们介绍了紧光滑流形M的向量场X的渐近轨道伪轨道跟踪性质的概念。我们证明如果向量场X具有\（C ^ 1 \）鲁棒渐近轨道伪轨道跟踪属性，则它是Anosov，并且如果\（C ^ 1 \）泛型向量场X具有渐近轨道伪轨道跟踪属性-orbit跟踪属性，则为Anosov。此外，我们还展示了无散度矢量场和哈密顿系统的结果。