A flipped family of alpha-continued fractions
|Dates:||14 May 2019|
|Times:||15:00 - 16:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, External researchers, Adults, Alumni, Current University students|
Join us for this research seminar, part of the Analysis and dynamics seminar series.
Continued fractions offer a representation of real numbers that is in many ways more natural that the canonical decimal representation. Among the many generalisations, the alpha-continued fractions were introduced in 1981 by Nakada as a family of interval maps depending on a parameter alpha. Since then, numerous studies have been done on the maps' metric and ergodic properties. In particular, the entropy has been studied as a function of the parameter: explicit intervals on which it is constant, increasing or decreasing have been characterised by the matching index of alpha and 1-alpha. We present a natural counterpart to the alpha-continued fractions. For this new collection of maps, we show, using a natural extension, that the (Krengel) entropy is constant, and we describe the matching intervals through the regular continued fraction expansions of alpha.
This is a joint work with Charlene Kalle, Niels Langeveld and Sara Munday.
Organisation: Universiteit Leiden
Biography: See Marta Maggioni's profile:
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Alan Turing Building