Study of transfer operator for geodesic flow and the semiclassical zeta function

2014 Fiscal Year Final Research Report

• Project/Area Number: 22340035
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kyushu University
• Principal Investigator: TSUJII Masato 九州大学, 数理(科)学研究科(研究院), 教授 (20251598)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 力学系 / 測地流 / カオス / 転送作用素 / スペクトル / エルゴード理論

Outline of Final Research Achievements

In this research project, we studied dynamical systems exhibiting typically chaotic behavior (especially, the geodesic flow which describes the motion of free particle on negatively curved space) and develop a theory to understand their fine statistical properties by analyzing spectral properties of associated transfer operators. The main result obtained in this research project proves that, for geodesic flows on negatively curved manifolds (or more generally for contact Anosov flows) the generator of transfer operators has discrete spectrum and has a band structure, that is, the discrete eigenvalues are contained in several bands parallel to the complex plane. Further we obtained the corresponding results on dynamical zeta functions. This is a significant progress in the related fields.

Free Research Field

力学系理論