Entropy and Complexity of Polygonal Billiards with Spy Mirrors

We prove that a polygonal billiard with one-sided mirrors has zero topological entropy. In certain cases we show sub exponential and for other polynomial estimates on the complexity

On the Hausdorff dimension of the Rauzy gasket

In this paper, we prove that the Hausdorff dimension of the Rauzy gasket is less than 2. By this result, we answer a question addressed by Pierre Arnoux. Also, this question is a very particular case of the conjecture stated by S.P. Novikov and A. Ya. Maltsev in 2003.Comment: 23 pages, 5 figure