We will establish several arithmetic and geometric properties regarding the bi-sequences of approximation coefficients (BAC) associated with the two one-parameter families of piecewise-continuous Möbius transformations introduced by Haas and Molnar. The Gauss and Renyi maps, which lead to the expansions of irrational numbers on the interval as regular and backwards continued fractions, are realized as special cases. The results are natural generalizations of theorems from Diophantine approximation.
0642: Theoretical Mathematics
Identifier / keyword
Pure sciences, Bi-sequences of approximation coefficients, Gauss maps, Mobius transformations, Renyi maps
The Bi-sequences of Approximation Coefficients for Gauss-like and Renyi-like Maps on the Interval
DAI-B 73/04, Dissertation Abstracts International
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Country of publication
University of Connecticut
United States -- Connecticut
Dissertations & Theses
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