The Hausdorff dimension of the level sets of Takagi's function

作者：de Amo E^*; Bhouri I; Diaz Carrillo M; Fernandez Sanchez J

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(15): 5081-5087.

DOI：10.1016/j.na.2011.05.001

• Takagi's function
• Level set
• Box counting
• Hausdorff dimension

Recently, Maddock (2006) [12] has conjectured that the Hausdorff dimension of each level set of Takagi's function is at most 1/2. We prove this conjecture using the self-affinity of the function of Takagi and the existing relationship between the Hausdorff and box-counting dimensions.

• 出版日期2011-10