# Metric theory for a new family of continued fraction expansions

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Niels Langveld

created by daniele on 16 Feb 2015

18 feb 2015
-- 14:30

Sala Riunioni, Collegio Puteano, Centro de Giorgi, Pisa

Seminari di Sistemi Dinamici Olomorfi, Pisa

**Abstract.**

The family of flipped expansions and the family of 2-expansions is
combined to make a new family of continued fraction expansions we will
call flipped 2-expansions. It is shown that there is only one flipped
continued fraction expansion map that will produce only even digits and
only one map which will produce only odd digits. Similarly we find only
one map for which the 2-expansion of every number will have odd digits.
When combining, we obtain for every real number infinitely many
expansions with only odd or only even digits. Some examples of flipped
2-expansions are given and a method for finding the invariant measure
using the natural extension is explained.
This work is the result of my graduation project supervised by Cor Kraaikamp.