Analytical studies of irrationally indifferent cycles in higher dimensional complex dynamics and Diophantine approximations

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740087
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kyoto Institute of Technology
• Principal Investigator: OKUYAMA Yusuke 京都工芸繊維大学, 工芸科学研究科, 准教授 (00334954)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 複素力学系 / 数論力学系 / 無理的中立周期系 / ディオファントス近似

Outline of Final Research Achievements

We established a quantitative asymptotically Fekete property of averaged pullbacks of points up to an exceptional set of capacity 0 under the dynamics of a rational function of degree >1 on the Berkovich projective line over an algebraically closed field that is complete with respect to a non-trivial absolute value and has characteristic 0, and characterized and established an equidistribution theorem for moving targets in terms of Diophantine approximation. On the other hand, as an application of Diophantine property of critical orbits, we solved a problem posed by Favre--Dujardin on an approximation of the bifurcation current of a holomorphic family of rational functions and the activity current of a marked critical point of the family in the case of superattracting periodic points.

Free Research Field

複素力学系、数論