动力系统

The theory of dynamical systems began with H. Poincaré’s work of qualitative theory of ODEs. A main objective of this theory is to understand the structure and properties of the solutions of a given ODE system (and hence to see how the system shall evolve). This course will begin with some simple ODE systems on the plane, the basic concepts such as attractor/repeller, hyperbolic set, stable/unstable manifolds, and also some related results shall be introduced. Later on, some selected topics such as chaotic dynamics and the N-body problem shall be studied. Also, this course will present and discuss on some examples of discrete dynamical systems, e.g. the shift map on a shift space, interval maps and Anosov isomorphisms on torus.