CODING CHAOTIC BILLIARDS .2. COMPACT BILLIARDS DEFINED ON THE PSEUDOSPHERE

We study ''a la Morse coding'' of compact billiards defined on the pseudosphere. As for most bounded systems, the coding is non-exact (except for the non-generic case of tiling billiards). However, two sets of approximate grammar rules can be obtained, one specifying forbidden codes, and the other allowed ones. In-between some sequences remain in the ''unknown'' zone, but their relative amount can be reduced to zero as one lets the length of the approximate grammar rules go to infinity. The relationship between these approximate grammar rules and the ''pruning front'' introduced by Cvitanovic et al. is discussed.