Nakada, Hitoshi

写真a

Affiliation

Faculty of Science and Technology （Mita）

Position

Professor Emeritus

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Career 【 Display / hide 】

  • 1978.04
    -
    1981.03

    慶應義塾大学（工学部数理工学科） ,助手

  • 1981.04
    -
    1985.03

    慶應義塾大学（理工学部数理科学科） ,助手

  • 1985.04
    -
    1990.03

    慶應義塾大学（理工学部数理科学科） ,専任講師

  • 1988.10
    -
    1990.09

    慶應義塾大学理工学部（数理科学科） ,学習指導副主任

  • 1990.04
    -
    1999.03

    慶應義塾大学（理工学部数理科学科） ,助教授

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Academic Background 【 Display / hide 】

  • 1973.03

    Keio University, Faculty of Engineering, 管理工学科

    University, Graduated

  • 1975.03

    Keio University, Graduate School, Division of Engineering, 管理工学専攻

    Graduate School, Completed, Master's course

  • 1978.03

    Keio University, Graduate School, Division of Engineering, 管理工学専攻

    Graduate School, Withdrawal after completion of doctoral course requirements, Doctoral course

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Academic Degrees 【 Display / hide 】

  • 工学　, Keio University, 1981.03

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Research Areas 【 Display / hide 】

  • Natural Science / Basic analysis

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Papers 【 Display / hide 】

  • On the Legendre and the Lenstra constants for complex continued fractions introduced by J. Hurwitz

    Nakada H.

    Acta Arithmetica （Acta Arithmetica)  196 （ 3 ） 269 - 289 2020

    ISSN  00651036

  • On the construction of the natural extension of the Hurwitz complex continued fraction map

    Ei H., Ito S., Nakada H., Natsui R.

    Monatshefte fur Mathematik （Monatshefte fur Mathematik)  188 （ 1 ） 37 - 86 2019.01

    ISSN  00269255

    　View Summary

    © 2018, Springer-Verlag GmbH Austria, part of Springer Nature. We consider the Hurwitz complex continued fraction map associated to the Gaussian field Q(i). We characterize the density function of the absolutely continuous invariant measure for the map associated to the Hurwitz continued fractions. For this reason, we construct a representation of its natural extension map (in the sense of an ergodic measure preserving map) on a subset of C× C. This subset is constructed by the closure of pairs of the n-th iteration of a complex number by the Hurwitz complex continued fraction map and -QnQn-1, where Qn is the denominator of the n-th convergent of the Hurwitz continued fractions. The absolutely continuous invariant measure for the natural extension map is induced from the invariant measure for Möbius transformations on the set of geodesics over three dimension upper-half space. Then the absolutely continues invariant measure for the Hurwitz continued fraction map is given by its marginal measure.

  • A Piecewise rotation of the circle, IPR maps and their connection with translation surfaces

    Inoue K., Nakada H.

    Lecture Notes in Mathematics （Lecture Notes in Mathematics)  2213   393 - 431 2018

    ISSN  00758434

    　View Summary

    © Springer International Publishing AG, part of Springer Nature 2018. For given positive integers dj, 1 ⩽ j⩽ ∀ s, ∑j=1sdj even, we construct a piecewise rotation map of the circle with ∑j=1sdj+s discontinuous points such that its critical iterates generate translation surfaces with singularity orders dj, 1 ⩽ j⩽ s, and with any Rauzy class associated to this singularity orders. The construction of the piecewise rotation map is combinatorial, on the other hand, the construction of the translation surfaces is based on the idea by Cruz and da Rocha.

  • Farey maps, Diophantine approximation and Bruhat-Tits tree

    Kim Dong Han, Lim SeonheeNAKADA HITOSHI, Natsui Rie

    Finite Fields and their Applications 30   14 - 32 2014.11

    Research paper (scientific journal), Joint Work, Accepted

    　View Summary

    形式的べき級数に関する Farey map を Bruhat-Tits tree の中で表現した。また、Farey map に関するエルゴード理論的性質をいくつか証明した。

  • On the equivalence relations of α-continued fractions

    NAKADA HITOSHI, Natsui Rie

    Indagationes Mathematicae 25 （ 4 ） 800 - 815 2014.06

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  0019-3577

    　View Summary

    α-連分数の同値関係が α が減少するにつれて群作用の同値関係とどのように異なっていくかを示した。

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Presentations 【 Display / hide 】

  • エルゴード的変換の同型問題とその不変量としてのエントロピー--- old and new

    NAKADA HITOSHI

    電子回路設計と力学系 (京都大学数理解析研究所) , 

    2015.09
    , 

    Oral presentation (invited, special)

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    エルゴード理論における同型問題と符号化理論の発展に関する講演を行った。

  • On the dual map of Rauzy induction

    NAKADA HITOSHI

    Workshop on Measurable and Topological Dynamical Systems (National Institute of Mathematical Scioences, Daejon, Korea) , 

    2015.07
    , 

    Oral presentation (general)

    　View Summary

    Rauzy induction の dual map の構成について解説した。

  • How to find the absolutely continuous invariant measures for continued fraction maps

    NAKADA HITOSHI

    Ergodic Theory and Combinatrics (University of Agder, Kristiansand, Norway) , 

    2015.06
    , 

    Oral presentation (invited, special)

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    連分数変換の絶対連続不変測度がどのように導かれるかについて講演を行った。

  • On the natural extension of the Rauzy-Veech induction

    NAKADA HITOSHI

    Ergodic Theory and Dynamical Systems -- Torun 2014 (Nicolaus Copernicus University, Torun, Poland) , 

    2014.05
    , 

    Oral presentation (invited, special)

    　View Summary

    Rauzy induction の逆に対応するzippered rectanglesに対するinductionについて講演を行った。

  • On the notion of normal numbers for alpha continued fractions

    NAKADA HITOSHI

    Probability,Ergodic Theory, Dynamical Systems (Tel Aviv University, Tel Aviv, Israel) , 

    2014.04
    , 

    Oral presentation (invited, special)

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    α連分数に対する正規数の概念がαに独立に定まることを紹介した。

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • グラフ構造の幾何学的表現の解析による数論的変換のエルゴード理論

    2020.04
    -
    2023.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

  • 無限大不変測度を持つエルゴード的変換の多重再帰性とエルデシ予想

    2016.04
    -
    2019.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Challenging Exploratory Research, Principal investigator

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Memberships in Academic Societies 【 Display / hide 】

  • Mathematical Society of Japan

    　
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Committee Experiences 【 Display / hide 】

  • 2015.06
    -
    2015.07

    organizer, Workshop on Measurable and Topological Dynamical Systems

  • 2014.01

    organizer, Warwick-Keio Seminar in Ergodic Theory

  • 2013.06

    organizer of the specialsession "Measurable and Topological Dynamics", Pacific Rim Mathematical Association Congress 2013

  • 2010.04
    -
    2011.03

    プロジェクト研究組織委員, 京都大学数理解析研究所

  • 2010.03

    2010年度年会実行委員長, 日本数学会

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