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The Brjuno function was introduced by Yoccoz to study the linearizability ofholomorphic germs and other one-dimensional small divisor problems. The Brjunofunctions associated with various continued fractions including the by-excesscontinued fraction were subsequently investigated: it was conjectured that thedifference between the classical Brjuno function and the even part of theBrjuno function associated with the by-excess continued fraction extends to aH\"older continuous function of the whole real line. In this paper, we provethis conjecture and we extend its validity to the more general case of Brjunofunctions with positive exponents.  Moreover, we study the Brjuno functions associated to the odd and evencontinued fractions introduced by Schweiger. We show that they belong to all$L^p$ spaces, $p\ge1$. We prove that the Brjuno function associated to the oddcontinued fraction differs from the classical Brjuno function by a H\"oldercontinuous function. On the other hand, the Brjuno function associated to theeven continued fraction differs from the classical Brjuno function by a sum ofa H\"older continuous function and a Brjuno-type function associated to theodd-odd continued fraction, introduced in the study of the best approximationsof the form odd/odd.

The Brjuno functions of the by-excess, odd, even and odd-odd continued fractions and their regularity properties