Title of article :
The Hausdorff dimension of the level sets of Takagi’s function
Original Research Article
Author/Authors :
E. de Amo، نويسنده , , I. Bhouri Baouab، نويسنده , , M. D?az Carrillo، نويسنده , , J. Fern?ndez-S?nchez، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
Abstract :
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.
Keywords :
Level set , Box counting , Takagi’s function , Hausdorff dimension
Journal title :
Nonlinear Analysis Theory, Methods & Applications
Journal title :
Nonlinear Analysis Theory, Methods & Applications
