Displaying similar documents to “Generalized continued fractions and orbits under the action of Hecke triangle groups”

Transcendence with Rosen continued fractions

Yann Bugeaud, Pascal Hubert, Thomas A. Schmidt (2013)

Journal of the European Mathematical Society

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We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.

Continued fractions on the Heisenberg group

Anton Lukyanenko, Joseph Vandehey (2015)

Acta Arithmetica

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We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.

Rosen fractions and Veech groups, an overly brief introduction

Thomas A. Schmidt (2009)

Actes des rencontres du CIRM

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We give a very brief, but gentle, sketch of an introduction both to the Rosen continued fractions and to a geometric setting to which they are related, given in terms of Veech groups. We have kept the informal approach of the talk at the Numerations conference, aimed at an audience assumed to have heard of neither of the topics of the title. The Rosen continued fractions are a family of continued fraction algorithms, each gives expansions of real numbers in terms of elements...