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arXiv:1302.6121 [math.NT]AbstractReferencesReviewsResources

Continued fractions on the Heisenberg group

Anton Lukyanenko, Joseph Vandehey

Published 2013-02-25, updated 2013-05-22Version 2

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. We then discuss dynamical properties of the associated Gauss map, comparing them with base-$b$ expansions on the Heisenberg group and continued fractions on the complex plane.

Comments: Version 2 introduces significant changes to the text, especially Section 4 on the dynamical properties of the Heisenberg Gauss map
Categories: math.NT, math.DS, math.GR, math.MG
Subjects: 22E40, 11J70, 53C17
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