一类带重叠的斜积的不稳定方向和维数
Unstable directions and dimension for a class of skew products with overlaps
摘要：
我们研究了一类在纤维中具有重叠的斜积，并证明了在这种情况下，即使对于原映射的扰动，非稳定流形也确实依赖于前历史。利用反压力、Cantor集的厚度和原像计数函数的某些界，给出了局部极大不变集纤维的豪斯多夫维数的几个结果.
英文摘要：
We study a class of skew products with overlaps in fibers and show that in this case the unstable manifolds really depend on prehistories, even for perturbations of the original maps. We also give several results about the Hausdorff dimension of the fibers of the respective locally maximal invariant set, by using the inverse pressure, the thickness of Cantor sets and some bounds for the preimage counting function.
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