Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 8 (2013), 59 -- 76


Santanu Chaktaborty

Abstract. There have been quite a few generalizations of the usual continued fraction expansions over the last few years. One very special generalization deals with θ-continued fraction expansions or simply θ-expansions introduced by Bhattacharya and Goswami [1]. Chakraborty and Rao [3] subsequently did elaborate studies on θ-expansions in their paper. They also obtained the unique invariant measure for the Markov process associated with the generalized Gauss transformation that generated θ-expansions for some special θs. In this work, we investigate an interesting question regarding the nature of θs for θ-expansion of 1/θ terminating at stage two, particularly with θ rational.

2010 Mathematics Subject Classification: 11J70; 37A45; 37E05.
Keywords: θ-expansions; Generalized Gauss map; Invariant measure.

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Santanu Chaktaborty
University of Texas-Pan American,
1201 West University, Edinburg, Tx, 78541, USA.