Construction and application of a theory of dynamical systems on complex surfaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740096
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Saga University (2014-2015); Niigata University (2012-2013)
• Principal Investigator: Uehara Takato 佐賀大学, 工学(系)研究科(研究院), 准教授 (40613261)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 複素曲面 / 力学系 / 有理曲面 / エントロピー / ディターミナント / ジーゲル領域

Outline of Final Research Achievements

We study dynamical systems of biholomorphic automorphisms on rational surfaces with positive topological entropy. We determine explicitly the determinant values, which are defined for automorphisms preserving anticanonical curves, and show the existence of an abundance of rational surface automorphisms with positive entropy. Moreover, we show the existence of automorphisms on complex surfaces with positive entropy having a given number of Siegel domains, which are observed around fixed points.

Free Research Field

複素力学系, 代数幾何学