TY - JOUR
T1 - How inhomogeneous Cantor sets can pass a point
AU - Li, Wenxia
AU - Wang, Zhiqiang
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/11
Y1 - 2022/11
N2 - For x> 0 , let Υ(x)={(a,b):x∈Ea,b,a>0,b>0,a+b≤1},where Ea,b is the unique nonempty compact invariant set generated by the inhomogeneous IFS Ψa,b={f0(x)=ax,f1(x)=b(x+1)}.We show that the set Υ (x) is a Lebesgue null set with full Hausdorff dimension and the intersection of the sets Υ (x1) , … , Υ (xℓ) still has full Hausdorff dimension for any finite number of positive numbers x1, … , xℓ.
AB - For x> 0 , let Υ(x)={(a,b):x∈Ea,b,a>0,b>0,a+b≤1},where Ea,b is the unique nonempty compact invariant set generated by the inhomogeneous IFS Ψa,b={f0(x)=ax,f1(x)=b(x+1)}.We show that the set Υ (x) is a Lebesgue null set with full Hausdorff dimension and the intersection of the sets Υ (x1) , … , Υ (xℓ) still has full Hausdorff dimension for any finite number of positive numbers x1, … , xℓ.
KW - Cantor set
KW - Hausdorff dimension
KW - Inhomogeneous
KW - Intersection
KW - Thickness
UR - https://www.scopus.com/pages/publications/85136974135
U2 - 10.1007/s00209-022-03099-0
DO - 10.1007/s00209-022-03099-0
M3 - 文章
AN - SCOPUS:85136974135
SN - 0025-5874
VL - 302
SP - 1429
EP - 1449
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3
ER -