On Bowen’s problem #17
Yuri Lima (UFC)
Rufus Bowen (1947-1978) left a notebook with 157 problems in dynamics, ranging in a huge variety of subjects. On problem #17, he wrote “symbolic dynamics for billiards". This question remained wide open until the early nineties, when Bunimovich, Chernov and Sinai constructed Markov partitions for the Liouville measure in dispersing billiards. Recently, Carlos Matheus and I constructed much more general Markov partitions, that work for a larger class of billiards (e.g. the stadium billiard) and of measures (e.g. the ones recently constructed by Baladi and Demers). In this talk I will explain the general framework of our proof, as well as the main difficulties encountered.