Regularity properties of Brjuno functions associated with by-excess, odd and even continued fractions

Abstract: An irrational number is called a Brjuno number if the sum of the series of $\log(q_{n+1})/q_n$ converges, where $q_n$ is the denominator of the $n$-th principal convergent of the regular continued fraction. The importance of Brjuno numbers comes from the study of one variable analytic small divisor problems. In 1988, J.-C. Yoccoz introduced the Brjuno function which characterizes the Brjuno numbers to estimate the size of Siegel disks. In this talk, we introduce Brjuno-type functions associated with by-excess, odd and even continued fractions with a number theoretical motivation. Then we discuss the $L^p$ and the Hölder regularity properties of the difference between the classical Brjuno function and the Brjuno-type functions. This is joint work with Stefano Marmi.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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