Morphisms preserving the set of words coding three interval exchange

Any amicable pair \phi, \psi{} of Sturmian morphisms enables a construction of a ternary morphism \eta{} which preserves the set of infinite words coding 3-interval exchange. We determine the number of amicable pairs with the same incidence matrix in $SL^\pm(2,N)$ and we study incidence matrices associated with the corresponding ternary morphisms \eta.Comment: 16 page

Do species differ in their ability to coexist with the dominant alien Lupinus polyphyllus? : A comparison between two distinct invaded ranges and a native range

The community-level impacts of invasive plants are likely to vary depending on the character of native species of the target communities and their ability to thrive within the stands of the dominant alien invader. Therefore, I examined the response of native species richness to the cover of the dominant alien Lupinus polyphyllus in two distinct invaded ranges: Czech Republic (Central Europe) and New Zealand. I compared the relation between native species richness and the cover of the dominant alien L. polyphyllus with that in its native range, Pacific Northwest, USA. In the native range, I found no response of native species richness to the cover of L. polyphyllus. In the Czech Republic (central Europe), the richness of native species related to it negativelly, but the relation was only marginally significant. Contrary to that, the richness of species native to New Zealand related to the cover of L. polyphyllus strongly negatively and the negative relation was significantly stronger than that of species native to Europe. Of the two invaded ranges, species native to New Zealand have been documented to be much more vulnerable to the conditions associated with the invasion and dominance of L. polyphyllus, compared to species native to central Europe. This principle has been shown both across these two invaded ranges and in New Zealand, where the aliens of european origin successfully coexist with the dominant invasive alien L. polyphyllus. Similarly, species in the native range of L. polyphyllus showed no relation to its cover, indicating their ability to thrive even in dense stands of this dominant species

Balancedness of Arnoux-Rauzy and Brun words

We study balancedness properties of words given by the Arnoux-Rauzy and Brun multi-dimensional continued fraction algorithms. We show that almost all Brun words on 3 letters and Arnoux-Rauzy words over arbitrary alphabets are finitely balanced; in particular, boundedness of the strong partial quotients implies balancedness. On the other hand, we provide examples of unbalanced Brun words on 3 letters