Self-similar structure on intersections of triadic Cantor sets
نویسندگان
چکیده
منابع مشابه
Self-similar Measures and Intersections of Cantor Sets
It is natural to expect that the arithmetic sum of two Cantor sets should have positive Lebesgue measure if the sum of their dimensions exceeds 1, but there are many known counterexamples, e.g. when both sets are the middle-α Cantor set and α ∈ ( 1 3 , 1 2 ). We show that for any compact set K and for a.e. α ∈ (0, 1), the arithmetic sum of K and the middle-α Cantor set does indeed have positive...
متن کاملOn Intersections of Cantor Sets: Hausdorff Measure
We establish formulas for bounds on the Haudorff measure of the intersection of certain Cantor sets with their translates. As a consequence we obtain a formula for the Hausdorff dimensions of these intersections.
متن کاملRandom Intersections of Thick Cantor Sets
Let C1, C2 be Cantor sets embedded in the real line, and let τ1, τ2 be their respective thicknesses. If τ1τ2 > 1, then it is well known that the difference set C1 − C2 is a disjoint union of closed intervals. B. Williams showed that for some t ∈ int(C1−C2), it may be that C1∩ (C2 + t) is as small as a single point. However, the author previously showed that generically, the other extreme is tru...
متن کاملCorrelation dimension for self-similar Cantor sets with overlaps
We consider self-similar Cantor sets Λ ⊂ R which are either homogeneous and Λ− Λ is an interval, or not homogeneous but having thickness greater than one. We have a natural labeling of the points of Λ which comes from its construction. In case of overlaps among the cylinders of Λ, there are some “bad” pairs (τ, ω) of labels such that τ and ω label the same point of Λ. We express how much the co...
متن کاملSelf-Similar Markov Processes on Cantor Set
We define analogues of Brownian motion on the triadic Cantor set by introducing a few natural requirements on the Markov semigroup. We give a detailed description of these symmetric self-similar processes and study their properties such as mixing and moment asymptotics.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2008
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2007.03.089