Itineraries induced by exchange of three intervals

Zuzana Masáková, Edita Pelantová, Štěpán Starosta

Itineraries induced by exchange of three intervals

Číslo: 6/2016
Periodikum: Acta Polytechnica
DOI: 10.14311/AP.2016.56.0462

Klíčová slova: interval exchange transformation; three gap theorem; return time; first return map, Transformace výměny intervalu; Doba návratu; První návratová mapa

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Anotace: We focus on a generalization of the three gap theorem well known in the framework of exchange of two intervals. For the case of three intervals, our main result provides an analogue of this result implying that there are at most 5 gaps. To derive this result, we give a detailed description of the return times to a subinterval and the corresponding itineraries.