5 papers · 1 filter
Exact dimensionality of projected measures for expanding rational semigroups
Yuto Nakajima
We study the dimension theory of expanding rational semigroups. An expanding rational semigroup is naturally described by a skew product on the product of the symbolic space and th…
Fractal transference principle for continued fractions of Laurent series
Yuto Nakajima
We establish a fractal transference principle for continued fraction expansions over the field of Laurent series. Let be an infinite subset of the set of all polynomials over a…
Topology of slices through the Sierpiński tetrahedron
Yuto Nakajima, Takayuki Watanabe
We investigate slices of the Sierpiński tetrahedron from a topological viewpoint. For each , we study the Čech (co)homology group of the slice at height . We show tha…
How many points contain homothetic copies in their Hurwitz continued fraction expansion?
Yuto Nakajima, Hiroki Takahasi
We prove that the set of complex irrationals whose partial quotients in their Hurwitz continued fraction expansion are naturally regarded as subsets of and contain in…
A problem of Hirst for the Hurwitz continued fraction and the Hausdorff dimension of sets with restricted slowly growing digits
Yuto Nakajima, Hiroki Takahasi
We address the problem of determining the Hausdorff dimension of sets consisting of complex irrationals whose complex continued fraction digits satisfy prescribed restrictions and…