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2019 Fiscal Year Annual Research Report

Analytic study of irrationally indifferent cycles in higher dimensional complex dynamics and non-archimedean dynamics

Research Project

Project/Area Number 15K04924
Research InstitutionKyoto Institute of Technology

Principal Investigator

奥山 裕介  京都工芸繊維大学, 基盤科学系, 教授 (00334954)

Project Period (FY) 2015-04-01 – 2020-03-31
Keywords複素力学系 / 非アルキメデス的力学系 / 無理的中立周期系
Outline of Annual Research Achievements

Hyperbolic components of rational maps: Quantitative equidistribution and counting. Commentarii Mathematici Helvetici, 94, Issue 2 (2019), 347-398 においては Thomas Gauthier, Gabriel Vigny 両教授と共同でd次有理関数のリヤプノフ指数の局所一様定量的近似公式を確立し、応用として複素力学系の正則族のモヂュライにおける非交後方分岐周期的類集合の分岐測度への定量的等分布定理およびそのような類の個数の分岐測度の体積を用いた漸近的数え上げ公式を確立した。A generalization of the converse of Brolin’s theorem. Annales Polonici Mathematici, 123 (2019), 467-472 においては Malgorzata Stawiska 教授と共同でBrolinの定理の逆と見なされる、有理関数全体において多項式をその平衡測度で特徴付けるLopesの定理の最良の一般化を、複素平面代数幾何におけるOlevkovのレムニスケート既約性定理の応用として得た。Geometric formulas on Rumely’s weight function and crucial measure in non-archimedean dynamics. Mathematische Annalen, 376, Issue 3 (2020), 913-956 においてはRumelyにより導入されたBerkovich射影直線上の非アルキメデス的力学系における種々の代数的同変量をBerkovich双曲幾何的に研究しそれらの精密化を与えた。

  • Research Products

    (5 results)

All 2020 2019 Other

All Int'l Joint Research (1 results) Journal Article (3 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 3 results) Presentation (1 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Int'l Joint Research] Universite de Picardie Jules Verne/Universite de Lille/Ecole Polytechnique(フランス)

    • Country Name
      FRANCE
    • Counterpart Institution
      Universite de Picardie Jules Verne/Universite de Lille/Ecole Polytechnique
  • [Journal Article] Geometric formulas on Rumely’s weight function and crucial measure in non-archimedean dynamics2020

    • Author(s)
      Yusuke Okuyama
    • Journal Title

      Mathematische Annalen

      Volume: 376 Pages: 913-956

    • DOI

      10.1007/s00208-019-01884-7

    • Peer Reviewed
  • [Journal Article] Hyperbolic components of rational maps: Quantitative equidistribution and counting2019

    • Author(s)
      Thomas Gauthier, Yusuke Okuyama, and Gabriel Vigny
    • Journal Title

      Commentarii Mathematici Helvetici

      Volume: 94 Pages: 347-398

    • DOI

      10.4171/CMH/462

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A generalization of the converse of Brolin's theorem2019

    • Author(s)
      Yusuke Okuyama and Malgorzata Stawiska
    • Journal Title

      Annales Polonici Mathematici

      Volume: 123 Pages: 467-472

    • DOI

      10.4064/ap180819-23-2

    • Peer Reviewed / Int'l Joint Research
  • [Presentation] A generalization of the converse of Brolin's theorem2019

    • Author(s)
      Yusuke Okuyama
    • Organizer
      Geometric Complex Analysis on Foliations and Dynamics
    • Int'l Joint Research / Invited

URL: 

Published: 2021-01-27  

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