Symbolic dynamics and number theory for tent maps and beta transformations. (English) Zbl 1132.37304
Summary: Our goal in this paper is to present some results which relate symbolic dynamics associated to iterated maps of the interval and number theory. The study is based on the orbit structure of piecewise linear maps, tent map and \(\beta\)-transformations.
MSC:
| 37B10 | Symbolic dynamics |
| 37E05 | Dynamical systems involving maps of the interval |
| 37A45 | Relations of ergodic theory with number theory and harmonic analysis (MSC2010) |
| 11R06 | PV-numbers and generalizations; other special algebraic numbers; Mahler measure |
