| Budget Amount *help |
¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2014: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2010: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| 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.
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