Abstract
Schweiger introduced the notion of a subtractive algorithm, to classify certain types of multidimensional continued fractions. We study the limit behaviour of one particular subtractive algorithm, which generalises a continued fraction algorithm that was originally proposed by Selmer. The algorithm that we study depends on two parameters a and b. We first find a Markov partition if a ≥ b. Using inducing techniques, we then prove the existence of an ergodic absolutely continuous invariant probability measure a ≥ b for the quality of the rational approximations for Lebesgue-typical multidimensional vectors.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
