论文标题
奇怪的吸引者为保存lozi地图的定向家庭
Strange attractors for the family of orientation preserving Lozi maps
论文作者
论文摘要
我们扩展了Michal Misiurewicz的结果，以确保存在参数化家族的奇怪吸引子$ \ {f _ {（a，b）} \} $方向的$ comprestation revession revers corvers lozi映射到定向案例。也就是说，我们严格地确定了吸引子$ \ Mathcal {a} _ {（a，b）} $ $ f _ {（a，b）} $始终存在并展示混乱属性的参数空间的开放子集。此外，我们证明吸引子在某个开放的参数区域中是最大的，并且作为固定点的不稳定歧管的闭合而出现，$ f _ {（a，b）} | _ {\ Mathcal {a} _} _ {a} _ {（a，b）}} $是混合的。我们还表明，$ \ Mathcal {a} _ {（a，b）} $在Hausdorff Metric中与参数$（a，b）$连续变化。
We extend the result of Michal Misiurewicz assuring the existence of strange attractors for the parametrized family $\{f_{(a,b)}\}$ of orientation reversing Lozi maps to the orientation preserving case. That is, we rigorously determine an open subset of the parameter space for which an attractor $\mathcal{A}_{(a,b)}$ of $f_{(a,b)}$ always exists and exhibits chaotic properties. Moreover, we prove that the attractor is maximal in some open parameter region, and arises as the closure of the unstable manifold of a fixed point, on which $f_{(a,b)}|_{\mathcal{A}_{(a,b)}}$ is mixing. We also show that $\mathcal{A}_{(a,b)}$ vary continuously with parameter $(a,b)$ in the Hausdorff metric.
