Critical itineraries of maps with constant slope and one discontinuity

Michael Barnsley (1) , Wolfgang Steiner (2) , Andrew Vince (3)

1 ANU - Australian National University
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 UF - University of Florida [Gainesville]

For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of $\beta$-expansions (with positive or negative $\beta$) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is provided.

Domaines: Systèmes dynamiques [math.DS]

Michael Barnsley, Wolfgang Steiner, Andrew Vince. Critical itineraries of maps with constant slope and one discontinuity. Mathematical Proceedings of the Cambridge Philosophical Society, 2014, 157 (03), pp.547-565. ⟨10.1017/S0305004114000486⟩. ⟨hal-01188674⟩