7 papers
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 SierpiÅski tetrahedron
Yuto Nakajima, Takayuki Watanabe
We investigate slices of the SierpiÅski tetrahedron from a topological viewpoint. For each , we study the Äech (co)homology group of the slice at height . We show t…
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…
Hausdorff dimension of sets of numbers whose continued fractions contain arbitrarily long arithmetic progressions
Yuto Nakajima, Hiroki Takahasi, Baowei Wang
Continued fractions with prescribed structures on sequences of their partial quotients have been intensively studied in the literature. As far as an integer sequence, especially a…
Density combinatorics theorems in fractal dimension theory of continued fractions
Yuto Nakajima, Hiroki Takahasi
We build a bridge from density combinatorics to dimension theory of continued fractions. We establish a fractal transference principle that transfers common properties of subsets o…