6 papers
Rate distortion dimension of Gibbs measures for functions depending on the first two coordinates on the full shift of Ahlfors regular spaces
Kanji Inui, Mao Shinoda
The study on shift spaces in ergodic theory has extended beyond the classical setting, but there is room to discuss an extension of the Kolmogorov-Sinai entropy in the ergodic theo…
Pointwise regularity and irregularity of energy densities on -dimensional Sierpinski gaskets
Masanori Hino, Kanji Inui, Kohei Nitta
We study the pointwise regularity of energy densities associated with harmonic functions on the -dimensional Sierpinski gasket with respect to the Kusuoka measure. Fo…
Understanding the limit sets generated by general iterated function systems on unbounded spaces
Kanji Inui
In this paper, we reformulate the definition of the iterated function systems (denoted by general IFSs in this paper) and show the existence and uniqueness (in some sense) of the l…
Packing measure and dimension of the limit sets of IFSs of generalized complex continued fractions
Kanji Inui, Hiroki Sumi
We consider a family of conformal iterated function systems (for short, CIFSs) of generalized complex continued fractions. Note that in our previous paper we showed that the proper…
Hausdorff measures and packing measures of the limit sets of CIFSs of generalized complex continued fractions
Kanji Inui, Hiroki Sumi
We consider a family of CIFSs of the generalized complex continued fractions with a complex parameter space. We show that for each CIFS of the family, the Hausdorff measure of the…
The Hausdorff dimension function of the family of conformal iterated function systems of generalized complex continued fractions
Kanji Inui, Hikaru Okada, Hiroki Sumi
We consider the family of CIFSs of generalized complex continued fractions with a complex parameter space. This is a new interesting example to which we can apply a general theory…