Title: Recurrent and periodic points for isometries of L^\infty spaces

Authors: Ege Fujikawa and Katsuhiko Matsuzaki

Issue: Volume 55 (2006), Issue 3, 975-998

Abstract: We study the action of isometries on metric spaces. In particular, we consider the recurrent set of the bilateral shift operator on the Banach space $L^{\infty}(\mathbb{Z})$, and prove that the set of periodic points is not dense in the recurrent set. Then we apply this result to investigating the dynamics of Teichm\"uller modular groups acting on infinite dimensional Teichm\"uller spaces as well as composition operators acting on Hardy spaces.