1 citations · 2 across the 10 of their papers we have counts for
11 papers
On the Ordering and Injectivity of Lagrange Constants Associated with Certain Substitutions
Shin-ichi Yasutomi
Motivated by the modern characterization of the Markoff spectrum via mechanical words and the Markoff Uniqueness Conjecture, we study the Lagrange constants of continued fractions…
Periodic points in complex continued fractions by J. Hurwitz
Shin-ichi Yasutomi
J. Hurwitz introduced an algorithm that generates a continued fraction expansion for complex numbers , where the partial quotients belong to .…
Simultaneous Convergent Continued Fraction Algorithm for Real and -adic Fields with Applications to Quadratic Fields
Shin-ichi Yasutomi
Let be a prime number and be a field with embeddings into and . We propose an algorithm that generates continued fraction expansions converging i…
Arithmetical independence of certain uniform sets of algebraic integers
Asaki Saito, Jun-ichi Tamura, Shin-ichi Yasutomi
We study four (families of) sets of algebraic integers of degree less than or equal to three. Apart from being simply defined, we show that they share two distinctive characteristi…
Star-shaped trajectories of certain billiards around a triangle
Takeo Noda, Shin-ichi Yasutomi, Masamichi Yoshida
We explore the triangle outer billiards map in points at infinity in the hyperbolic plane, focusing on the rotation number. Building on Dogru and Tabachnikov's work, which establis…
Billiards in a circle with trajectories circumscribing a triangle
Takeo Noda, Shin-ichi Yasutomi
Dogru and Tabachnikov in 2003 explored the polygonal outer billiard map in the hyperbolic plane and introduced a class of convex polygons called 'large'. They particularly sought c…
A remark on Chapple-Euler Theorem in non Euclidean geometry
Takeo Noda, Shin-ichi Yasutomi
In non-Euclidean geometry, there are several known correspondings to Chapple-Euler Theorem. This remark shows that those results yield expressions corredponding to the well-known f…
Ergodicity for -adic continued fraction algorithms
Hui Rao, Shin-ichi Yasutomi
Following Schweiger's generalization of multidimensional continued fraction algorithms, we consider a very large family of -adic multidimensional continued fraction algorithms,…
Multidimensional -adic continued fraction algorithms
Asaki Saito, Jun-ichi Tamura, Shin-ichi Yasutomi
We give a new class of multidimensional -adic continued fraction algorithms. We propose an algorithm in the class for which we can expect that multidimensional -adic version…
Continued fraction algorithms and Lagrange's theorem in
Asaki Saito, Jun-ichi Tamura, Shin-ichi Yasutomi
We present several continued fraction algorithms, each of which gives an eventually periodic expansion for every quadratic element of over and gives a…
A new multidimensional slow continued fraction algorithm and stepped surface
Maki Furukado, Shunji Ito, Asaki Saito +2
We give a new algorithm of slow continued fraction expansion related to any real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find th…