Study of functional analytic methods in dynamical system theory

我们研究了动力系统理论和遍历理论中的泛函分析方法。对于双曲和部分双曲动力系统，我们在相空间上构造了与系统相适应的函数空间，使得相应的转移算子在其上具有良好的谱性质。作为应用，我们得到了关于负曲流形上的动力zeta函数的Ruelle-Pollicott共振和解析性质的精确结果，特别是对于扩张半流和测地线流.

We studied functional analytic methods in dynamical systems theory and ergodic theory. For hyperbolic and partially hyperbolic dynamical systems, we constructed function spaces on the phase space adapted to the system so that the corresponding transfer operators have good spectral properties on them. As an application, we get precise results on Ruelle-Pollicott resonance and analytic properties of dynamical zeta functions especially for expanding semi-flows and geodesic flows on negatively curved manifolds.