Dynamical Systems Seminar

主講者: Dr. Sergey Tikhomirov (National Taiwan University)
講題: Program for Numerical Simulations of Dynamical Systems
時間: 2010-01-19 (Tue.)  15:00 - 16:00
地點: 數學所 714 研討室 (台大院區)
Abstract: I am going to present software program for numerical simulation of dynamical systems. The purpose of the program is approximating of the invariant manifolds of a hyperbolic periodic orbit and their intersections. Near such intersections system usually admits chaotic behavior. The main idea of the method is the following. Iterations of a disk transversal to the stable manifold of a periodic orbit tends to the unstable manifold. We represent iterations of the disk as a union of simplexes. During iterations we control the maximal size of a simplex. By the theorem mentioned above those iterations tends to unstable manifold. Points of intersections of simplexes of stable and unstable manifolds correspond to homoclinic points. This is joint work with G. Osipenko and M. Senkov. 
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