Fractal Analysis of Transport Properties in a Sinai Billiard

Research contacting chaos with fractals is carried out. First, we employ the theoretical quarter Sinai billiard model to study its chaos by using the stationary expansion method. When the billiard is chaotic, the singular point shows self-similarity. We further utilize the method of simplified box counting to calculate the fractal dimension. The result evidently proves the self-similarity of the singular point before escaping from a potential well.