On positive braids motivated by Rossler dynamical system

Rossler positive braids are defined and denoted by Rm+. We represented a general form of Rossler positive braid, and its associated permutation. For the mm period Rossler positive braid Rm+, the number of crossing equals to [2(m-2)+(m-1)][2(m-2)+(m-1)], and the genus g  (Rm+)=(m-2), it also has a braid index equals to mm, m>1m>1.