The paper concerns the mean hyperbolicity of the skew-product flows induced by the perturbation equations driven by varieties of non-periodic forcings. The weakly averaged horseshoe can be constructed as a mean hyperbolic invariant set in the Poincare section for high dimensional phase space. Due to the non-periodic property, the Poincare return map restricted to the weakly averaged horseshoe region can semi-conjugate to the full Bernoulli shift on infinite symbols, which implies the infinitely many independent choices on the length of return time. As a direct application of mean hyperbolicity, we extend the shadowing lemma due to Liao to the general nonautonomous dynamical systems.

该论文涉及由各种非周期性强迫驱动的扰动方程引起的斜积流的平均双曲线性。弱平均马蹄铁可以构造为高维相空间的 Poincare 部分中的平均双曲不变量集。由于非周期性质，限制在弱平均马蹄形区域的庞加莱回报图可以半共轭到无限符号上的完整伯努利位移，这意味着在返回时间长度上有无限多个独立选择。作为平均双曲线的直接应用，我们将 Liao 的阴影引理扩展到一般的非自治动力系统。