Geometry and dynamics of systems with a hyperbolic flavor

该建议的目标是促进研究和培训HQP在理论数学领域的交叉动力系统，几何和低维拓扑。我的研究计划重点关注两个不同的问题亚族。第一个涉及的理解和拓扑分类的某些类型的动力系统在流形的低维。第二个是关于一系列的问题之间的相互作用的动力学性质的系统的几何起源（测地流的芬斯勒或黎曼流形是最重要的），几何或光谱数据来自度量。

The goal of this proposal is to promote research and the training of HQPs in domains of theoretical mathematics at the intersection of dynamical systems, geometry and low dimensional topology. My research program focuses on two distinct subfamilies of questions. The first involves the understanding and topological classification of certain types of dynamical systems in manifolds of low dimension. The second is concerned with a range of questions regarding the interactions between the dynamical properties of systems of geometrical origin (the geodesic flow of a Finsler or Riemannian manifold being the foremost), and geometric or spectral data coming from the metric.