|Date||Nov 18, 2022|
An irrational number is called a Brjuno number if the sum of the series of converges, where is the denominator of the n-th principal convergent of the regular continued fraction. The importance of Brjuno numbers comes from the study of analytic small divisor problems in dimension one. 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 (negative), odd and even continued fractions. Then we discuss the 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.