The Rauzy Gasket

Pierre Arnoux (1) , Starosta Štěpán (2, 3)

1 I2M - Institut de Mathématiques de Marseille
2 FNSPE - Department of Mathematics [Prague]
3 Department of Theoretical Computer Science and Mathematical Logic [Prague]

We define the Rauzy gasket as a subset of the standard two-dimensional simplex associated with letter frequencies of ternary episturmian words. We prove that the Rauzy gasket is homeomorphic to the usual Sierpiński gasket (by a two-dimensional generalization of the Minkowski ? function) and to the Apollonian gasket (by a map which is smooth on the boundary of the simplex). We prove that it is also homothetic to the invariant set of the fully subtractive algorithm, hence of measure 0.

Domaines: Systèmes dynamiques [math.DS]

Pierre Arnoux, Starosta Štěpán. The Rauzy Gasket. Birkhäuser Boston. Further Developments in Fractals and Related Fields, Springer Science+Business Media New York, pp.1-23, 2013, Trends in Mathematics, 978-0-8176-8399-3. ⟨10.1007/978-0-8176-8400-6_1⟩. ⟨hal-01265693⟩