Morphisms preserving the set of words coding three interval exchange

Abstract

Any amicable pair ϕ , ψ of Sturmian morphisms enables a construction of a ternary morphism η which preserves the set of infinite words coding 3-interval exchange. We determine the number of amicable pairs with the same incidence matrix in SL± (2,ℕ) and we study incidence matrices associated with the corresponding ternary morphisms η .