• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

A study on the dynamics of two dimensional polynomial skew products

Research Project

Project/Area Number 21540203
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionTokyo Polytechnic University

Principal Investigator

NAKANE Shizuo  東京工芸大学, 工学部, 教授 (50172359)

Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords複素解析 / 複素力学系 / Axiom A / skew product / base Julia集合 / fiber Julia集合 / saddle basic set / relation / holomorphic motion / polynomial skew product / base Julia set / solenoid / 危点集合 / 安定多様体 / 不安定多様体
Research Abstract

Investigating the link between postcritical behaviors and the relations of saddle basic sets for Axiom A polynomial skew products on C2, we characterized some properties of the three kinds of accumulation sets of the critical set in terms of the saddle basic sets. We also showed that these properties are preserved in the hyperbolic components. We gave an example with a property characteristic to the higher degree maps.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (26 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (14 results) (of which Peer Reviewed: 7 results) Presentation (10 results) Remarks (2 results)

  • [Journal Article] Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C22013

    • Author(s)
      中根静男
    • Journal Title

      Ergodic Theory and Dynamical Systems

      Volume: 33 Issue: 4 Pages: 1124-1145

    • DOI

      10.1017/s0143385712000193

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A novel method for evaluating postsurgical results of unilateral cleft lip and palate with theuse of Hausdorff distance.2012

    • Author(s)
      Toru Yanagawa, Shizuo Nakane, et.al
    • Journal Title

      Oral Surg OralMed Oral Pathol Oral Radiol

      Volume: Vol.114 Issue: 6 Pages: 704-711

    • DOI

      10.1016/j.oooo.2012.01.042

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Presurgical nasoalveolar molding orthopedic treatment improves the outcome of primary cheiloplasty of unilateral complete cleft lip and palate, as assessed by naris morphology and cleft gap.2012

    • Author(s)
      Toru Yanagawa, Shizuo Nakane, et.al.
    • Journal Title

      Journal of Craniofacial Surgery

      Volume: Vol. 23 Issue: 6 Pages: 1596-1601

    • DOI

      10.1097/scs.0b013e31825196dc

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On saddle basic sets forAxiom A polynomial skew products on C^2.2012

    • Author(s)
      Shizuo Nakane
    • Journal Title

      数理解析研究所講究録

      Volume: Vol. 1807 Pages: 66-73

    • Related Report
      2012 Final Research Report
  • [Journal Article] On saddle basic sets for Axiom A polynomial skew products on C^22012

    • Author(s)
      Shizuo Nakane
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1807 Pages: 66-73

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Presurgical nasoalveolar molding orthopedic treatment improves the outcome of primary cheiloplasty of unilateral complete cleft lip and palate, as assessed by naris morphology and cleft gap2012

    • Author(s)
      Hiroyoshi Sasaki
    • Journal Title

      Journal of Craniofacial Surgery

      Volume: 23 Pages: 1596-1601

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C^2.2011

    • Author(s)
      Shizuo Nakane
    • Journal Title

      数理解析研究所講究録

      Volume: Vol. 1762 Pages: 114-119

    • Related Report
      2012 Final Research Report
  • [Journal Article] Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C^22011

    • Author(s)
      Shizuo Nakane
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1762 Pages: 114-119

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Component-wise accumu- lation sets for Axiom A polynomial skew products.2010

    • Author(s)
      Shizuo Nakane
    • Journal Title

      数理解析研究所講究録

      Volume: Vol. 1699 Pages: 81-87

    • Related Report
      2012 Final Research Report
  • [Journal Article] Component-wise accumulation sets for Axiom A polynomial skew products2010

    • Author(s)
      Shizuo Nakane
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1699 Pages: 81-87

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Remarks on Axiom A poly- nomial skew products of higher degrees.2009

    • Author(s)
      Shizuo Nakane
    • Journal Title

      Proceedings of ICFIDCAA

      Volume: Vol.16 Pages: 196-200

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Branner-Hubbard- Lavaurs deformations for real cubic poly- nomials with a parabolic fixed point.2009

    • Author(s)
      Shizuo Nakane
    • Journal Title

      Conformal Geometry and Dynamics

      Volume: Vol. 13 Issue: 5 Pages: 110-123

    • DOI

      10.1090/s1088-4173-09-00192-1

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Branner-Hubbard-Lavaurs deformations for real cubic polynomials with a parabolic fixed point2009

    • Author(s)
      Shizuo Nakane
    • Journal Title

      Conformal Geometry and Dynamics 13

      Pages: 110-123

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on Axiom A polynomial skew products of higher degrees2009

    • Author(s)
      Shizuo Nakane
    • Journal Title

      Proceedings of 16^<th> ICFIDCAA

      Pages: 196-200

    • Related Report
      2009 Annual Research Report
  • [Presentation] On saddle basic sets for Axiom A polynomial skew products on C2. RIMS 研究集会2012

    • Author(s)
      Shizuo Nakane
    • Organizer
      複素力学系の総合的研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-01-26
    • Related Report
      2012 Final Research Report
  • [Presentation] On saddle basic sets for Axiom A polynomial skew products on C^22012

    • Author(s)
      Shizuo Nakane
    • Organizer
      研究集会「複素力学系の総合的研究」
    • Place of Presentation
      京都大学数理解析研究所(招待講演)
    • Year and Date
      2012-01-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Postcritical sets and saddle basic sets for Axiom A polynomialskew products on C2. RIMS 研究集会2010

    • Author(s)
      Shizuo Nakane
    • Organizer
      複素 力学系とその周辺分野の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-12-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C^22010

    • Author(s)
      Shizuo Nakane
    • Organizer
      研究集会「複素力学系とその周辺分野の研究」
    • Place of Presentation
      京都大学
    • Year and Date
      2010-12-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C2.2010

    • Author(s)
      Shizuo Nakane
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C^22010

    • Author(s)
      Shizuo Nakane
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dynamics of Axiom Apolynomial skew products2010

    • Author(s)
      Shizuo Nakane
    • Organizer
      国際数学者会議
    • Place of Presentation
      インド, ハイデラバード
    • Year and Date
      2010-08-24
    • Related Report
      2012 Final Research Report
  • [Presentation] Dynamics of Axiom A polynomial skew products2010

    • Author(s)
      Shizuo Nakane
    • Organizer
      国際数学者会議2010
    • Place of Presentation
      ハイデラバード
    • Year and Date
      2010-08-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] 複素力学系とその 関連分野の総合的研究 RIMS 研究集会2009

    • Author(s)
      Shizuo Nakane
    • Organizer
      Component-wise accumu- lation sets for Axiom A polynomial skew products.
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-12-16
    • Related Report
      2012 Final Research Report
  • [Presentation] Component-wise accumulation sets of critical sets for Axiom A polynomial skew products2009

    • Author(s)
      中根静男
    • Organizer
      研究集会「複素力学系とその関連分野の総合的研究」
    • Place of Presentation
      京都大学
    • Year and Date
      2009-12-16
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.gen.t-kougei.ac.jp/math/nakane/index.html

    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://www.gen.t-kougei.ac.jp/math/nakane.index.html

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi