55 citations · 174 across the 35 of their papers we have counts for
35 papers
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…
Non-i.i.d. random holomorphic dynamical systems and the generic dichotomy
Hiroki Sumi, Takayuki Watanabe
We consider non-i.i.d. random holomorphic dynamical systems whose choice of maps depends on Markovian rules. We show that generically, such a system is mean stable or chaotic with…
The Dynamics and Geometry of Semi-Hyperbolic Rational Semigroups
Jason Atnip, Hiroki Sumi, Mariusz Urbański
We study skew-product dynamics for a large class of finitely-generated semi--hyperbolic semigroups of rational maps acting on the Riemann sphere, which generalizes both the theory…
Multifractal Formalism for generalised local dimension spectra of Gibbs measures on the real line
Johannes Jaerisch, Hiroki Sumi
We refine the multifractal formalism for the local dimension of a Gibbs measure supported on the attractor of a conformal iterated functions system on the real line. Namely…
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…