Definition of "Contractive Invariant Plane"

Question

Can someone please explain the definition of a contractive invarient Plane found in: the paper

It is nearly at the very beginning of the Introduction. By contractive do they mean a contractive map? Even if they do, I don't understand what they would mean by this.

Thanks

Answer 1

See: http://www.shunjiito.com/paper/ArnouxIto.pdf I do not understand why he uses the phrase 'Contractive Invariant Plane', but it seems to mean the plane which is orthogonal to the Perron Eigenvector of the incidence matrix of the substitution. The two other eigenvectors live inside that plane also. In the wikipedia of Rauzy Fractals, I see the word 'contractive' for the plane in the picture they have, but i'm not sure what it actually means.